This Christmas season I’ve noticed a few folks mixing up the stable in which Luke claims Jesus was born with the manger he is said to have been laid in.
A manger is an animal feed trough. The word comes from the French word for “eat.” It is not a sort of building. A manger can also take the form of a V-shaped feeder called a crib. The role such a manger plays in the Christmas story probably influenced the use of “crib” to designate a child’s bed.
A stable is the building animals and occasional humans are sheltered in; the manger is a feature of the stable.
Matthew says nothing of all this, of course.
For a good discussion of the two birth stories, see this page at errancy.org.