For starters, you'll probably want to read
this. It's a great set of tutorials on synthesis that'll help make a lot of other things clear. Most keyboards use these principles: even if you're using a realistic string sound, the keyboard underneath is using things like envelopes and LFOs (if you don't know what those are, go through that tutorial, at least the general ones before they start talking about how to mimic certain sounds, and it'll become clear), so even if you don't get a synthesizer, knowing this still helps.
Something else that would help you, at least with a better keyboard, is reading a bit about effects (you'll probably have the best luck searching google for guitar effects, but the principles are the same, even if guitarists used many of them first). This would include EQ, reverb, compressor, wah, overdrive/distortion, and so on.
Understanding the different types of keyboards is pretty straightforward. Ignoring all the really low end stuff, you have five main classes of keyboards. Workstation keyboards are the ones that have a wide variety of pre-sampled sounds - strings, pianos/keyboards, some synthesized sounds, brass, and such. Workstations may have samplers (letting you record or make use of your own pre-sampled sounds) and sequencers (letting you record individual tracks to make a song on the keyboard). The idea here is that they've prerecorded one or more samples (short audio clips) for each sound, and are applying synthesis techniques to shape that sample.
There are also arranger keyboards, which are often similar to workstations but also will play along with you using one of the various styles on the keyboard (or one you create yourself). I've never really liked them; I'd rather just have a workstation keyboard.
Next, there are stage pianos and digital pianos (including the ones that are shaped like a small upright piano). They usually have very few sounds and are usually best for someone who wants to just sit down and play piano. The choir you play for is in a new rehearsal space without a piano tonight? A stage piano is the way to go. Some get more complicated than that - my Nord Stage is a stage piano with a fairly large number of piano and electric piano sounds, an organ section with full drawbar control, and a simple but usable synthesizer.
MIDI controllers are keyboards that don't actually make sound. They send MIDI data to another keyboard or to a computer, and that other keyboard or computer produces the sound. Your M-Audio keyboard would be this type.
Lastly, synthesizers. Like I said, many of the other types of keyboards use the principles of synthesis, but they're not synthesizers in the same sense. Something classified as a synthesizer won't rely strictly on pre-sampled waves. Instead, you have a wave generator, which generates an audio signal, but unlike a sample, the signal can be changed in certain ways. I'll let the synthesis tutorial I linked explain it better and in more detail.
As for new keyboard recommendations, it really depends what you want to do. Nowadays, with a decent computer, the music you can produce will outclass what you can do on a keyboard, but there are benefits, particularly with synthesizers, to having hardware and not software - being able to control and program the synth with dedicated knobs is really nice, and hardware is usually more portable than a computer (though I bring my two keyboards and laptop along with me sometimes when I play - I did build a custom cabinet/stand to house my amp and provide a flat surface for my laptop though).
So, what kind of keyboard do you want? Well, you've said that weighted keys are important and you do electronic music. You probably have no use for a stage piano or arranger, so the question is whether to get a workstation, synth, or both.
Synths make up the bulk of electronic music, but having some other sounds might be nice too, and that overcomes the limitations of a single synth (very few synths let you use any kind of sample, plus sampling is, honestly, a pain). Synths almost never have weighted keys, don't usually have sequencers (so no recording the tracks for your songs), and usually have smaller keyboards - workstations tend to be 61, 73/76, or 88 keys (5, 6, and 7 octaves); synths are usually 25, 37, or 49 keys.
What I would suggest is to get a workstation, and if you can afford it, a synth to go along with it. As far as workstations go, the big players are Korg, Yamaha, and Roland. To me, Korg is a bit more natural to figure out, and Korg tends to be the best with synthesized sounds; Yamaha is usually the best at acoustic instruments, and I don't really like Roland.
Sticking with Korg, you've got three options for workstations, unless you go used. The OASYS is really expensive but is great. It lets you use the most effects, and really is a bunch of different engines under the hood that you can mix and match - an organ engine with drawbars, a few different types of synths, and a sampling engine. In the cheaper realm, the M50 and M3 are both really good, with the M3 being the better choice of the two - it has sampling built in, it's more solidly built, it has aftertouch (the keys send messages once they're pressed that indicate how much pressure is on them; keyboards can make small variations in the sound based on the aftertouch). In all three cases, you'd need the 88-key model to get weighted keys.
Another advantage of the M3, if you're also looking to get a synth, is that you can either get the EXB-RADIAS expansion, which adds the power of the Korg Radias synth to the M3, or you can get the Radias-R (the rack mount version of the Radias without a keyboard) and mount that on the M3 and have easy access to all its knobs. You get the same synth in either case; it's just a choice between better integration (you save a program or combi - a bunch of programs layered together - that uses the Radias, and then call it up easily on the M3; with the radias-R, you'd need a MIDI cable between the two in order to make the Radias change programs whenever you change your M3) and hardware control (the EXB-RADIAS is a small circuit board that goes inside your M3; once it's in, you never see it again, so there's clearly no knobs to turn).
