Is there a difference of substance between the veneration of Mary, and the worship of God? Speaking from a protestant understanding, I had just assumed that Catholics would say they worshipped Mary. 

They (often) pray to her, sing her praise (calling her holy, and such). Sometimes bowing to her, and constantly adorning her with titles (Blessed Mother, Queen of Heaven, Mother of God, etc etc.). Sometimes kneeling before her statues, etc. This from an outside perspective seemed like worship to me. And it was a thing they were very much proud of.

I was talking to a Catholic apologist at a local event as she passed out rosaries. She was trying to teach me the hail Mary, and convince me that I should pray to Mary. 

But when I used the word "worship" she recoiled, and claimed not to worship Mary. On this site I have had a similar reaction. I was surprised by this reaction.

If you just google search "worship" here is what you get. (the verb form)


  show reverence and adoration for (a deity); honor with religious rites.
  //"the Maya built jungle pyramids to worship their gods"//
  synonyms:   revere, reverence, venerate, pay homage to, honor, adore, praise, pray to, glorify, exalt, extol; More


The question

So, it seems that Catholics would agree that it is wrong to Worship Mary. Obviously they don't think of the things they are doing as worship. I am interested in the substance of "adoration/veneration/worship" that is appropriate for God alone, and that which appropriate for Mary or the saints.
A criteria by which one could judge a concrete example of adoration.


How do Catholics make this distinction?
What is Worship for a Catholic? And is it reserved for God alone?
How does this play out practically (what would it look like to worship God in light of this distinction)?
One useful distinction appears in petitionary prayer. We ask both Mary (as well as the other saints) and God to help us by doing things for us. The difference is in what we ask them to do.

For example, the prayer to Mary known as the Litany of Loreto begins by petitioning God in the Trinity, then moves to petitioning Mary, then back to God. But though both God and Mary are asked to do things, they're very different. We ask God:


  God the Father, have mercy on us.
  God the Son, Redeemer of the world, have mercy on us.


And later, 


  Lamb of God, you take away the sins of the world: grant us peace.


In contrast, to Mary we pray;


  Mother of Christ, pray for us.
  Seat of Wisdom, pray for us.
  Queen of the most holy Rosary, pray for us.


Only God has the power to grant us graces, and it is only Him whom we ask for actual things. Mary and other saints have no such power, and our reverence to them does not (should not) extend so far as to ask them for things. We can only ask them to pray to God for us.

You can see another difference, perhaps, in this example. Someone who looks up to another, who takes them as a life example and perhaps even thinks of them as a hero, will treat them with great respect and reverence. They may feel a certain sense of awe in their presence. But in the other hand, there's the sense of awe and wonder that many people feel when they look up at the stars, and confront the majesty of the universe. The two feelings are different (I contend) in kind, not just in scale. That's analogous to the difference between our feelings toward Mary and those we have toward God.