I will choose a best answer for this....

The boundaries have become hazy because many carols are used as hymns and there are many modern pieces which are written in the style of carols. The proper definitions are as follows (but many pieces might qualify as more than one type). A hymn is a religious song of worship and praise primarily designed to be sung as part of a church service. They are usually of fairly recent origin (or translated from traditional hymns). The words are generally an address or prayer to God. Examples might be "Oh come all ye faithful" (a translation of a traditional Latin hymn) and "Angels from the realms of glory". A carol was originally specifically a dance song, that is to say that it was sung whilst performing a dance, usually a round dance, of a religious or semi-religious nature. Many of them are traditional. Carols often have lines of verse (sung by one person) and a refrain. A good example is "I saw three ships", which alternates a verse and a refrain and is in 6/8 rhythm, to which it is almost impossible not to dance! A 'Christmas song' is a narrative song, not necessarily devotional but sometimes so, relating some aspect of the Christmas story. It may also include elements of praise (as in a hymn) and many carols are narrative also. "Away in a manger" and "Silent Night" are 'songs', rather than hymns, for example. The category may also include secular songs such as "Rudolph the Red-nosed Reindeer" and "Frosty the Snowman"! Often you will find all three types included in collections of Christmas Carols and therefore all are sometimes referred to loosely as 'carols', especially by carol singers going from door to door.

Christmas carol is a song or a couple of songs being sung by a group in front of the crowd or an audience. Christmas songs are the songs that we usually hear whenever the Christmas season is on its way. As it is in my country, you can usually hear Christmas songs whenever the months that ends in "ber," like September, starts. And you will hear them all through the next 5 or 6 months to come. Christmas hymn must be the songs being dedicated to Jesus Christ who's the main reason why people celebrate Christmas every year. As far as I know, hymn is a type of religious songs, so it must be a song that gives praise to Jesus as well. Knowing this, people must be singing a Christmas hymn even if it's out of season..lol ;-)

A Christmas carol is sung by a group. In the Philippines, it is usually done by a group of people with a common objective, singing a medley of Christmas songs in different houses and the owner of the house would give money to them. The usual pattern for this, 1st is a Christmas carol greeting the owner of the house, 2nd and next few songs are different Christmas songs and the last is a thank you song for the money received. A Christmas song on the other hand is any song with the theme of Christmas. While a Christmas hymn i think is the background music of a Christmas song. It is like an instrumental part of the song. I am not an expert with music but this is what I understand.