Well, I’ve mentioned them on more than a few occasions. Might have even explained it. But if I did, I never tagged the posts.
Amplification is a collection of spells loosely grouped around the notion of taking something in it’s current state, and boosting it to a greater degree without sacrificing it’s form. I got into amplification when studying music; same reason why most non-combatants would. In particular a lyre, which has very few strings, can have it’s frequency amplified or reduced using magic to gain access to a wider range of available notes. However, for a unicorn of my limited magical ability, it’s a very difficult process to do rapid-fire beyond just shifting octaves.
Manipulation is more of a catchall than a legitimate pool of magic. Pretty much anything that doesn’t fit anywhere else winds up being classified as some form of manipulation. I mean, technically all magic is manipulation so it’s really a misnomer, but eh. I began studying a little bit of manipulation in order to learn how to change the sounds notes make. Unlike amplification, which maneuvers best off of set intervals (like a 4C to a 5C), manipulation works best by traveling to adjacent notes (4C, 4C♯ 4D, and so forth). The closer the desired note is to the source, the better.
I play by weaving the two concepts together; using whichever method more easily reaches the note I need.