I nor my older siblings never got any such thing as an "allowance".
My parents spent as we wished when available, when reasonable. When I was a teen, if I wanted to go somewhere they gave me money then for what might be appropriate (plus when old enough I got to drive their cars). Until I got a job (which was late, BTW). My mother in particular is also EXTREMELY fond of gifts (Christmas is a nightmare of her buying for EVERYONE, even people she sees once a year), and back as a child she might go to the pharmacy and while there pick up a fun book or something. She loved doing that.
But we never got any such thing as a regular allowance.
Your mother sounds like me! I love buying gifts. We never had allowances either back in the 40s and 50s. My parents didn't earn a whole lot of money but we got along fine. Of course, I had a grandmother who spoiled me...