I live in the U.S and I hear them called both. My dad used "change jar". I typically use "coin jar", however now I use "piggy bank" with my little kids.

In the United States, I've heard them called both. I can't think of any difference. "Change," especially "spare change," generally means coins. Perhaps we use "change" when we feel like using an uncountable noun, and "coins" when we feel like using a countable noun.

I typically call such a jar a "change jar".

Or, of these two choices, a change jar. A piggy bank is more of an enclosed savings container (usually for children), but an open mouthed jar for stashing and grabbing pocket change on the kitchen table, for instance, is a change jar.

piggy bank