Most labels for "electronic" music are crap -- they aren't helpful, and there are no concrete definitions. Even the name "electronic" music is misleading since many of the songs are made with live instrumentation which is rearranged in some way...but so is half of what you hear on the radio, so what's the point?
There are some basic divisions between styles of "dance" music, but the finer details are hopelessly complicated:
"Techno" music is based on a 4/4 pattern, meaning that every beat in the bar is accented. In a club, you will find yourself wanting to naturally tap your foot on every beat: BOOM BOOM BOOM BOOM... Good starting artist: Underworld, especially Dubnobasswithmyheadman.
"House" music is based on a 2/4 pattern, meaning that every other beat is accented. In a club, you will find yourself wanting to naturally tap your foot with "pauses" in between...and often, you will hear either a lighter drum or a cymbal on the unaccented beat: BOOM swish BOOM swish... Good starting artist: Blue Six, Beautiful Tomorrow.
"Drum and bass" is based on a syncopated rhythm: the "bass" part (synth or a bass drum) is usually at a slower BPM than the snares and/or cymbals. I personally have no idea how you'd dance to that stuff without twitching, but your mileage may vary. Good starting artist: I don't stay current on that stuff, but Goldie's Timeless is a classic, and you may enjoy Photek as well. I've also heard good things about High Contrast.
Maybe someone who is more awake can explain "breakbeat" is lucid terms.
As for how to find music that you like...I would recommend listening to the webcasts of "Metropolis" (weeknights 7:30-10:00 PM PST) and "Nocturna" (weeknights 10:00 PM - 12:00 AM PST) on the KCRW feed -- they broadcast on iTunes, Windows Media Player, Winamp (Shoutcast), and Real. If you hear something you like, make a note about when you heard it...then go to their website to see the artist and album. (They post complete playlists, and also announce the tracks periodically during the show.) You won't hear as much of the "hard stuff," but it will give you a starting point.