Most people in the world don't call it Aspirin, as that's a registered trademark of Bayer AG. The trademark was voided in the U.S. during WWI and never re-granted.
Bayer holds the trademark for Aspirin (Capital A) in Canada (and others).
The trademark is void in the US (and others)
When Canadians that I know (incluidng me) say "aspirin" we mean very deliberately "Any kind of ASA - and if it's not the generic stuff you're some kind of weirdo who likes to waste money" - but we still call it aspirin.
Brand names don't, of course - they list ASA as an ingredient... but I've never in my life heard someone ask if I had any ASA.
Different experiences. The first time I had someone ask me for some, I was confused: I didn't know what it was (I had just immigrated from the US). But I've had more than a few people refer to it as ASA in the thirteen years I've been here.
Here in Canada, we call it ASA.