It's a bit of a mess, indeed. Just a quick rough rundown:
There's European parties (in EU parliament) and national parties (in each country).
Most national parties are affiliated with the european ones, so you can have for example three different national parties affiliated with the same european party.
Whenever you read "Social-democrat" or Green, they are lefties (S & D, Greens/EFA etc).
Then you have the conservatives centre-right (EPP) but these are establishment as well, just as the Liberals (ALDE).
Then there's Conservative-Eurosceptics (ECR, EFDD), and the Nationalist Movement (ENF).
There's whatever number of national parties affiliated with the above european ones – you'd have to look up for yourself.
The Guardian has a good list:
www.theguardian.com/world/ng-interactive/2019/may/26/eu-election-results-2019-across-europe
Also anon posted a nice map yesterday. I'm trying to find it in previous breads ….