Are Rounders and Baseball the same game?

Of course they re not. No more than rugby and American Football are the same game.

People that say they re the same know nothing about sport.

No more than checkers and chess are the same game.

It's more like softball than baseball because the bowler (pitcher) tosses the ball underhanded.

well, sort of. Maybe like stock car racing and formula 4. Badminton and tennis. Cricket and baseball.

The answer is "yes". The first-known reference to Rounders in the 1870's is that the game was called "baseball".

Mention of the equipment is pure nonsense. Neither game was standardised historically, so both versions had endless variations. Most people playing baseball and rounders in the early days used whatever was handy to whack the ball around.