I use the terms interchangeably when it comes to batteries; I do use battery disposal bins, but I don't have any faith that the actual process behind the scenes is much less impactful for the environment.

It's like when I learned that many paper recycling programs end up combining paper with regular garbage, or finding out that plastic recycling is comically ineffective in its outcomes.

Batteries in the trash are also a fire hazard. It's not just for the environment.