Yes, there is a difference between open and closed headphones.
Closed headphones have a cup behind the driver, sealing it off. The cup will block outside noise and also keep others from hearing what you're listening to.
Open headphones are open behind the driver. You will be able to hear some outside noise and people will be able to hear them.
It might sound like closed headphones have all the advantages, but there's a big drawback to having cups. Sound comes from the other side of the driver and it has to go somewhere. Some closed headphones do a good job of blocking and absorbing the sound coming from the back, but some don't.
If they don't do a good job, then you'll hear a reflection of that sound come back through the driver. Even if you do manage to damp them well, there are always a number of compromises with closed headphones, including a smaller soundstage.
Open headphones don't have problems with reflections. They're not perfect, but you usually get better fidelity from an open headphone.
Everyone wants a closed headphone when they first come here, but many switch to open after they've heard a few and enjoyed them.
Personally, I only have two closed pairs. The Sonys I like for airplanes and the DT48s are a somewhat oddball cult item that I happen to love.
I'd strongly recommend going with open headphones if you're going to listen at home. Closed are better for public areas and when you don't want to share your music with the person sitting next to you.
As for a recommendation, I'll go out on a limb and tell you to get the new Grado HF-2.
And I don't know what it is and neither does anyone else.
But the HF-1 was tremendously good value for the money and the HF-2 should be, as well. Also, they'll be difficult to find once the promotion ends. Moreover, you'll probably be able to sell them for more than you paid six months on.
