... and when is it correct to use the terms Gennaker and Drifter?
From Wiki, a Gennaker sounds just like an Asymm. Is that correct?
en.wikipedia.org
A gennaker is more of a cruising asymmetrical spinnaker, so a free flying luff. A drifter is a large and very light weight genoa. When I was a kid we had hanked on genoas. My dad bought a Mylar drifter with snaps instead of hanks. When the wind picked up the snaps would all pop off and we would hoist the #1 and do a peel.
Back to spinnakers, on a fat cruising boat a symmetrical spin will get you the best performance but will be harder to set up short handed. An asymmetrical is very fast on light weight boats that can build speed on a reach and get the apparent wind forward so can sail deeper. That's why you never see a sport boat with a symmetrical these days.
Asymmetrical spins cannot sail as deep down wind because the will be blanketed by the main, whereas a symmetrical can be pulled aft on the pole, getting it further out to windward in clear air.
Asymmetrical spins are easier to set and douse because you don't need to deal with a pole. You can put a sock on a symmetrical though which would take some of the drama out of it. On my old boat, a C&C27, I had a symmetrical because I raced it and that was what the class used. Also, it was not a light weight boat and would not have benefitted from a symmetrical when racing. On my Freeport 36 I went for an asym for two reasons. It is not rigged for a pole, and I wanted to fly it short handed.
With an asym you can add either a furler (generally top down) or a snuffer sock to make launching and retrieving easier. I got a screaming deal on an asym with a sock but I've sailed with both and I'd say the sock is a bit easier to use anyway. I have only had the boat for one summer and only got the spin up once but it was great to have it. It's like an extra gear when the wind goes aft of the beam. I have a 140% genoa but I sail with a 100% jib to make tacking and heavy weather sailing easier and the spinnaker makes a huge difference off the wind.