While there is some variation among the research, it's generally accepted that there are three main types of memory:
Tactile memory, generally considered the most fleeting, is the memory of automatic response. As muscle memory, it has little, if any, basis in the intellect, and it is learned by simple repetition. On the whole, tactile memory comes into play with extremely technical (read: fast) music. While it's often the first type of memory to be lost under pressure, it's also saved me in a number of instances when I couldn't see or hear what was coming next; thankfully, my fingers kept on going.
Aural memory is best when a musician has an excellent ear--and one can never have too good of an ear. While one may lose tactile memory, aural ability allows one to play by ear, anticipating upcoming pitches by "hearing" and finding those notes in advance. The memorization process will be greatly accelerated when one has already heard a piece many times--either by one's one playing or by hearing other performances. For this reason, memorizing a piece from scratch without having previously heard it can be a lengthy process.
Visual memory is exactly what it should be: seeing the music as you're playing it. This type of memory can be built entirely at the instrument, but it's most solid when learned away from the instrument. In my own practice, I tend to bring a piece to rough memory at the instrument (tactile and aural) and then move more and more away from the instrument to solidify my visual memory. At times, I'll start the visual process sooner, but in my own impatience, I tend to prefer playing the instrument instead of thinking about it. (That's my own problem. Don't make it yours!) When a program is good to go, however, I will spend at least half, if not two-thirds, of my time with a score, away from the instrument.
This leaves us with those subcategories. All three mentioned (structural, emotional, and linguistic) are created when practicing the main types of memory. Structural is based in musical form, and it needs to be tied to all three memory types from the beginning of the process. Emotional memory might have more to do with performance experience (and even anxiety). In my opinion, it doesn't hold a solid place in the practice room, although one must learn to manage and be aware of this type of memory. Finally, linguistic memory--the process of narratively guiding oneself through various cues and landmarks--is, for me, also a part of the three main types of memory. As it's based in cues and landmarks, it's closely tied to structural memory and, by association, the three main memory types.
Hopefully, this is about as scientific as I'll get in this blog, and, trust me, I'm not getting nearly as scientific as the hardcore research that's out there. If I could summarize the goal of my approach to memorization, it would be this:
I should be able to write out every memorized piece away from the instrument.
To do so, I would call upon my visual, my aural, and (even!) my tactile memory.