Poor defined as 'Any Poor' or 'Christian Poor' Context:

Proverbs 19:17


  He that hath pity upon the poor lendeth unto the LORD; and that which he hath given will he pay him again.


Luke 12:33


  Sell that ye have, and give alms; provide yourselves bags which wax not old, a treasure in the heavens that faileth not, where no thief approacheth, neither moth corrupteth.


... and plenty of more examples ...

In the Bible, when the Bible speaks of giving to / helping the poor, is the poor referred to as:

(1) any poor person
or
(2) a poor person that identifies him/herself as Christian

I.e. according to the Bible, should Christians give to poor non-Christians?
The word Poor is a translation from another word or words used in either the Old or New Testaments. It appears 201 times in the Bible in 194 different Verses.

The word poor is a translation from both Hebrew and Greek, and actually is several words in both the Old and New Testaments. The exact meaning of the word poor is dependent on what the original word was. That being said your question appears to only be concerned with where it is used in relation to the status of people, So let's look at some verses and see just how it is used:


  Genesis 41:19 KJV And, behold, seven other kine came up after them, poor and very ill favoured and leanfleshed, such as I never saw in all the land of Egypt for badness:


Here the word can in no way refer to Financial depravity since a Kine is a cow.


  Leviticus 14:21 NKJV  "But if he is poor and cannot afford it, then he shall take one male lamb as a trespass offering to be waved, to make atonement for him, one-tenth of an ephah of fine flour mixed with oil as a grain offering, a log of oil,


Here the word poor does in fact refer to the person's lack of earthly riches however:


  Matthew 5:3 NKJV  "Blessed are the poor in spirit, For theirs is the kingdom of heaven. 


Here the word translated poor can only refer to a man's Spiritual wealth. These are only examples but it shows that the word poor in translations into English, are dependent on what particular word was used in the original manuscript and the particular circumstance in which it is used.


  Matthew 11:5  The blind see and the lame walk; the lepers are cleansed and the deaf hear; the dead are raised up and the poor have the gospel preached to them. 


Here the word poor could be understood to refer to either or even both.

So in answer to your question, it is necessary to take the surrounding verses, and possibly the entire chapter, or even the whole book into consideration in determining the meaning of not only the word poor, but many other words used in modern translations. When you get to the point of trying to exact the meaning of certain words it necessitates that you study and not just read the Scriptures, and even then it is sometimes necessary to search out the original word in either Hebrew or Greek in order to fully understand what is being conveyed. Even after many years of studying the Bible there is much that still perplexes me.

Hope this helps.