cage vs batting cage

cage and batting cage both are nouns.

Word	Noun	Adjective	Verb	Adverb
cage	Yes	No	Yes	No
batting cage	Yes	No	No	No

As nouns, cage and batting cage are synonyms defined as:

cage and batting cage: a movable screen placed behind home base to catch balls during batting practice

cage (noun)	batting cage (noun)
an enclosure made or wire or metal bars in which birds or animals can be kept	a movable screen placed behind home base to catch balls during batting practice
the net that is the goal in ice hockey
a movable screen placed behind home base to catch balls during batting practice
something that restricts freedom as a cage restricts movement

cage (verb)	batting cage (verb)
confine in a cage