speck, cardioid and omni are two different "directional patterns" or "pickup patterns" that a microphone can be designed to have. The omni (short for "omnidirectional") is the simpler of the two: Regardless of what direction sound is coming from, the microphone will pick that sound up about equally well; it doesn't discriminate by the angle of arrival. Most omnidirectional mikes aren't perfectly true to this definition at high frequencies, but throughout the main part of their frequency range, it's how they work.
Omnidirectional microphones can have real advantages over microphones with other pickup patterns, but they work best under ideal acoustical conditions. OK, well, of course everything in the universe works best under ideal conditions--but what I mean is, if the space that you're recording in has a yummy balance of direct sound and reverberant (reflected) sound, and you put an omnidirectional microphone (or a pair of them for stereo) somewhere near where the two types of sound energy balance to your liking, the result can be quite beautiful. In a lousy room, though, the result can be quite lousy.
The other thing about omni mikes is that for stereo, you either have to space them apart a few feet or more, and/or put some kind of acoustically opaque object between them--or else they'll tend to pick up almost the exact same signals as each other (think about it!), and the result will be essentially a mono recording even though you used two microphones and two recorder channels to make it.
"Cardioid" is a pickup pattern in which the mike has greater sensitivity to sound that occurs in front of it than to sound that occurs beside it or especially, behind it. The microphone discriminates to a certain degree, in other words, depending on the angle at which the sound arrives at the microphone. This allows you to keep a pair of microphones close together and still get a stereo effect because you aim them apart from each other (with "front and center" bisecting the angle between their main axes, to get technical about it).
In a musical performance situation, when you aim cardioid microphones toward the main sources of direct sound, their backs will usually face (although why do we still call it "facing" when it's the backs of the microphones and they don't have faces anyway?) the back and/or sides of the room. Reflections come from there, but (usually) no direct sound unless there are pigeons in the eaves. As a result (deep breath now), cardioid microphones aimed at the direct sound sources will tend to pick up less reflected (reverberant) sound energy than omnidirectional microphones would pick up if they were placed at the same distance from the sound sources in the same room. The difference isn't night-and-day since a cardioid pattern is nothing like the narrow beam of a flashlight, but it's enough to notice. It allows a usable balance to be obtained at somewhat greater miking distances than an omnidirectional mike would allow, as well as in moderately terrible sounding rooms where a pair of spaced omni mikes would sound truly terrible as noted above.
There can be other differences but that's the most basic one. Good question, by the way.
--best regards