The word originally came from web-log, and it replaced a personal diary - meaning people kept an online record of their days.

That gradually morphed into their own websites or a blogging site where people still wrote their own stuff about their own lives, etc.

A writer, however, wrote for magazines, on content sites, did things like ghostwrite books for other people, etc. A writer did not write about their personal stuff, etc. That's what a blogger did. A writer is someone who earns their living professionally - full time - from writing.