It’s kinda hard to explain, but I’ll give it a go. -СЯ is a verb ending which is reflexive, meaning that the sufferer of the action is the same as the doer of the action. Let’s use a verb here: брить (to shave). Let’s add our reflexive ending. We get бриться (to shave oneself). So if I say он брил (he shaved, but referring to him shaving an object) it changes the meaning. So we say он брился because he shaved HIMSELF. Get it?
Now for себя. Себя is the reflexive pronoun. It can be translated in English as “oneself”. Now let’s kind of compare. I'll emphasize the reflexive pronoun or verb ending and emphasize its corresponding word in English.
Я увидела себя с тобой. (I saw myself with you.)
Я увиделась с тобой. (I went to see you/met up with you, I don’t know how to translate it — English is my third language.) This isn't really the best example, since I don’t know what it corresponds to in English, but I hope it helped :)