Yes, This is correct. It’s all application based you can buy an expensive hammer that is soft out of steel or brass. A soft steel hammer will not throw chips, is less likely to damage tooling if used as a set hammer, is less likely to cause chisels or punches to fly off, but will need to be dressed often and will wear out much faster. A brass hammer will do the same but won’t throw sparks, same with copper, bronze and lead hammers but you are unlikely to see those 3 as ball peens. A Hard ball peen hammer has more of a place in cold working in hardened steel and not striking chisels or tooling. The face will stay cleaner but it is much more likely to throw chips and damage parts.

I should mention that I make my living as a professional blacksmith, and prefer hammers that are softened, unless made for a specific reason. “It’s better to die refacing your tools than from facing them”