Criticize might be justified, or might not. Slagging someone is just taking them down, brutalizing on them, without regard. "You should pay better attention and stop being so lazy!" compare that to: "Oh, you're just no good, you've never been good, you'll never amount to anything." Slagging is a sophomoric trick, an immature game when you're smart enough to realize that it's a cheap thrill to slag on everyone and everything, but you haven't yet realized that it makes everyone hate you, including, eventually, yourself. Criticism can be positive, and encouraging. As the saying goes "A word to the wise is sufficient!" Meaning, it's good to tell someone when they make a mistake, but don't go on and on about it! The best way to deliver criticism- if you want people to really take hard criticism- is to cushion it in a 'sweet pill' of praise. For example: "You're very talented, and you do great work. But this project is all wrong, and it has to be fixed. I know you'll do a great job on it, let's talk about what has to happen."

Slag off is to critizice in a very rude manner, usually insulting by belittle way.

when you "slag off" someone, you apparently insulting him/her or turning them down. a slight sameness would be, they both finding fault with someone, but 'slag off' is very vulgar!