No the PSN is the online service for all playstation consoles. So it's the store and online gaming etc.
PS+ gives you 4/5 free games a month, a mix of PS3, 4 and Vita games. And it allows you to play online on the PS4. You don't need it to play online on the PS3.
Though any credit you buy is available across all your consoles, so if you put £50 credit into the store, you can the spend that on the PS3, PS4 or vita
Confused yet? lol
Yes a little So with my PS4, I only need PS+?