Battery question for flash unit

[AgX]

Hope this helps a link to battery size charts, what you may be calling the battery could be more accurately described as the "cell".
The "A" cell or battery is 50mm long and 17mm in diameter

Perfectly right, battery would be the term for a pack of cells OR a cell that actually is a disguised stack of cell in one primary container.
Anyway, over here the common term is battery.

I never came across type A cell.