- We usually say "Christmas presents."
In most cases, they are interchangeable, but not always.
For example, if you are really good at languages, I could say that you
have a gift for
languages. "Presents" would not work in that sentence.
Thinking about it in a way I've never done before, I guess a "present" is something you
present to someone, whereas a
gift is something you
give
to them in any way. We say
that you have a gift for languages because
God gave you that ability, but He did not wrap
it up in something and
present it to you.
- In most contexts, these two words can be used interchangeably.
Example:
birthday gift / birthday present
wedding gift / wedding present
Thanksgiving gift / Thanksgiving present
Christmas gift / Christmas present