These are 2 different things.
a VPS is a virtual private server
a VPN is a virtual private network
With a VPS you hire (lets say it easy) a computer standing in somebody elses house(its a server from a company), wich you controle with remote desktop software. (if its windows/linux is different)
So basiclly you dont have to run any osbot clients on your own laptop/computer that means you can let the VPS stay online for as long as you want no energy costs for you.
Also with that said you have a different IP on a VPS, since youre not running on your own computer/laptop.
With a VPN you install some kind of software on your computer, wich will replace your home IP into the IP the VPN is running on, so youre still running osbot on your own computer, and also have to buy a good VPN software (buy a good one, if you use free VPN the chance is the IP's are already flagged cuz of mass usage)
So basicly the VPN acts like a mask and will protect your internet data because its sended through secure servers.
To be honest, if you have a bit of knowledge just hire a VPS, it costs a bit more then a vpn but you can reach more with it, + you can run more bots, run a few on your VPS and run a few on your own pc
If you dont have any knowledge about linux, then you should go for a windows server VPS, then the only thing you have to do is login through remote desktop and done deal you can start right away.
I tryed to explain it as easy as possible, may have made a few mistakes but o well, english is not my mother language :P