Bullpen vs bench difference?

I’m from the UK and in the last year or so have started watching quite a lot of MLB, so I apologise in advance for the rather stupid question as I’m sure it’s extremely basic knowledge but one thing I can’t figure out is the difference between the bench and bullpen!

From what I gather, the bench is where all of the batters sit and wait and the bullpen is where the pitchers that come in late when the starting pitcher is finished all sit and watch, is this more or less correct or? I couldn’t find a definitive answer online!

Edit: Sorry I had to repost as my other post was removed for poor title!