Yes, it is the same animal. But, "bat" is what is used today. "Rearmouse" is an old term that most English speakers would not understand.

Hello! I actually had to look this up! I had never heard of a rearmouse before. We do not use this word in the United States for bats, but it does appear to be the same animal. The only references I see appear to be for British English. I only teach American English, so I can’t say whether or not this term is still common in the UK. Great question!

When I have gas, I blame it on the rearmouse.