What is the Biblical support for a distinction between veneration and worship? I was reading a question about icons, and this raised some questions for me.

Catholic and Eastern Orthodox beliefs hold to there being a difference between worship and veneration. What is the Biblical support for drawing a distinction between worship and veneration?

I was not able to find an answer on SE for this that does not rely on external sources.
To approach this question we must first cut through terminology.

The Catholic Dictionary defines worship as 


  Acknowledgment of another's worth, dignity, or superior position.


So worship is not, necessarily, religious at all. 

It then goes on to define two words for worship of a particularly religious character.


  In religion, worship is given either to God, and then it is adoration, or to the angels and saints, and it is called  veneration.


The basic definitions from the Oxford dictionary define worship as


  the feeling or expression of reverence and adoration for a deity  


(which is what Catholics mean by adoration)

and venerate as


  Regard with great respect; revere (i.e. feel deep respect or admiration for)


The King James Version generally regards worship as  having a wide connotation, similar to the Catholic definition of worship. The NIV uses worship only for worship of a (real or supposed) deity.

I take the OP's question to be asking for the difference between worship and veneration in the Oxford terminology; which is to say the difference between adoration and veneration in the Catholic terminology.

Either way, the distinction is simply that one relates to the worship of a deity, and the other does not. That is, quite simply, the difference. In a way, to answer the question, there is nothing more to be said. However there is a lot more that can be said.

We can consider some examples. When David grovelled to Saul (1 Samuel 24 8), and when Mephibosheth grovelled to David (2 Samuel 9 8) this was veneration, acknowledging the other's superior status. In Revelations 3 9 we are told that some who had been false would worship at the feet of the Philadelphian Christians, acknowledging that  they are the ones loved by God. It was surely not intended that members of the Philadelphian church should be worshiped as gods;  but rather that they be venerated as loved by God.   The worship of God described in Revelations 19 4 is adoration  because it is to God. The worship of Diana (Acts 19 27) is adoration, not mere veneration, because Diana, whatever her true status, was being worshiped as a deity.

A much lower form of the word worship appears in the Banquet (Luke 14 10) where the guest is advised to sit at the lower end of the table so  that when the host asks him up higher he will have worship (KJV). This does not, of course, mean the other guests will imagine him to be divine, or bow down to him, merely that he will go up somewhat  in their estimation. 

Before looking in more detail at the Bible it may be helpful to consider the concept of veneration in ordinary life.

We may attend church to worship God, by singing His praises, praying, contemplating His being and  listening attentively to His word. We may be impressed with the sermon, appreciating the message as inspiring , challenging, informative and useful.  We may think appreciatively of the amount of effort and study which the preacher has gone to, not just in preparing this sermon but in all the back years of study which enabled him to do this., We may be moved by the singing of the choir. In post-service fellowship we may enjoy a most delicious piece of cake, lovingly baked by a culinarily talented member of the flock. We may admire all these people, and remark favourably on them to others. We may personally speak to the preacher thanking him and praising him. We may do the same to the cakemaker  We may compliment one of the choirboys on his talent, diligence at practice, commitment and skill; all the while conscious that our own  abilities and efforts fall far short of his.

We would not think we were venerating the preacher, the baker or the musician, but that is what we would be doing. We would not bow down, as that is not in our culture, but we might express our admiration by physical gesture,  in other contexts, by  applauding with our hands. Applause is, in the wider sense, a form of worship.

We should not find that our appreciation of the cake got in the way of our worship of God, but if it did,  almost certainly it is our worship of God which is too low, rather than our veneration of the cake which is too high.  

Even animals, lacking words,  use gestures  to acknowledge status.

To turn now to worship in the New Testament; the most common word for worship is proskuneo (Strong's concordance word number 4352). This literally meant to kiss the ground in front of a person's feet as a mark of respect. This may mean anything from worshiping God to a conventional courtesy to a person of higher status.    Jairus (Matthew 9 18) and Mrs Zebedee (Matthew 20 20) were not worshiping Jesus as divine. The NIV translates proskuneo in these cases simply as knelt, though the KJV uses worship, reflecting the older usage. In the parable of the debtor (Matthew 18 26) the debtor falls to his knees and begs for time to pay. Again it is the same word, and the KJV translates it as worship. In general the NIV interprets the same word differently, depending on whether the perpetrator regards the recipient as divine.  That is the difference between worship (OP sense) and veneration, is neither more nor less than  to whom is it directed (or rather what does the doer think of that person). 

This same word is used to describe the Heavenly worship  in Revelations 19 4 and the worship of the Beast (Revelations 13 8).  

It is also the word used in John 4 20-24 where the Samaritan woman challenges Jesus as to why Jews worship only at the Temple. Here it seems to have a slightly higher meaning. After all, Jews worshipped in synagogues too, but the temple worship was special because it involved sacrifice. Similarly, it has been argued, true Christian worship, at its highest, requires participation in the sacrifice of the Mass.

A different Greek word latreia  (Strongs 2999) means more particularly service to God, the worship of God, and is translated in Romans 12 1 as true and proper worship in the NIV. This word is also used to refer in several places to the worship of God in the temple.  Philippians 3 3 has this as worship God in His Spirit in the KJV but  serve God by His Spirit in the NIV. 

In Acts 14 the priests of Zeus wanted to offer sacrifices to Paul and Barnabas, which led to them tearing their clothes and protesting strongly. This incident concerned an attempt to treat them as gods.

In Acts 10 25 Cornelius worshipped Peter (KJV) or did him reverence (NIV). Peter told him to stand up. There is no compelling reason to assume Cornelius intended to adore Peter as divine, rather than make a common gesture of polite respect.  Similarly Peter asking Cornelius to stand up is not, of itself, any argument that gestures of respect are wrong. It may simply be two men being mutually courteous to each other. It might be argued one way, it might be argued another. 

In Revelations John twice tries  to worship an angel, and is discouraged by that angel (Revelations 19 10 and Revelations 22 8). 

The worship of angels, referred to in Colossians 2 18, is based on a different Greek word, threskeia (Strong's 2356) which means  religion. What is being discussed here is a religion of angels, whatever that may have been.  

​The Church of England Article 22 states that the Roman doctrine concerning (amongst other things) worshiping, and adoration, of images and relics is grounded upon no warranty of Scripture. This being said, it is unlikely that any clear and convincing proof could ever be found to endorse such practices as being required by the Bible alone.  If there were such a clear unequivocal scriptural warrant could the C of E have failed to notice it? If one were subsequently deduced then, like the proof of Fermat's Last Theorem, it would be way too complicated for most of us  to comprehend.   However,  Roman Catholics and Eastern Orthodox do not ascribe to the Protestant "sola scriptura" (scripture alone) doctrine, but rather they teach that authoritative doctrine comes equally from the tradition of the Church. The Bible itself emerged from, and forms part of but not all of, that tradition.  Nowhere in the Bible is there a list of books which constitute the Bible, for example. The Church has decided .  Therefore the fact (if acknowledged)  that there is no proven warrant from scripture is not, from a Catholic or Orthodox perspective, reason to doubt the validity of a practice which is hallowed by centuries of Church tradition, and is found, in practice to increase devotion to, and worship of, God Himself.