Exactly, solo can mean 'alone' (He's alone / Él está solo) or something like 'just' or 'only' (El solo quiere eso / He only wants that). Solamente has the same meaning of the latter use (El solamente quiere eso). Since 2010, it is not necessary to use the tilde. The only time you need to use the tilde ( ' ) is when both uses of the word are acceptable and you need to specify wich one you intent, for example "El sólo hizo la cena / He only made dinner" would use tilde on sólo, but "El solo hizo la cena / He alone made dinner" would not use tilde.

The three are exactly the same. "Sólo" was the correct way to write it, now it is also accepted "solo". "Solamente" is just another way to say it.