Just starting to look into this myself...
Yes, for a level 2 240v connection, you need an EVSE that runs on 240v. The one that comes with your car is 110v by default, although as some have mentioned, it can be upgraded..
The tricky part is what type of connection.
Some type of EVSEs use plugs and different ones can use different plugs.
Some just get hardwared in...
What you probably want to do is get a few that you think you would like (match your price/option range) and have that info ready to talk with your electrician.
It's probably best to go with a plug for flexibility (if that's important to you), but you'll need to make sure that the receptacle your electrician puts in will be available for your EVSE model.
As for the 3 wire versus 4 wire thing, most (all?) of the higher end EVSEs don't use the 4th wire, but some of the receptacles might require it for code..
If you're going to the trouble to have someone else install a high amperage 240v receptacle, probably silly to skimp on the 1 wire.
Although, if the run is from your panel to the garage and that's REALLY REALLY far, cost-wise, it might make sense..
Good luck..
desiv
(and I am asuming you have a newer EV? I picked up a Leaf with the 3.3kW charger, so I can't take advantage of the benefits of the more powerful EVSEs. Which means I get to decide also do I put in a bigger circuit / EVSE now thinking I'll likely need it in 4 years or so anyway when I'm likely to trade up??? Choices.. ;-) )