Walk into any grooming aisle and you'll find a wall of jars, all claiming to do roughly the same thing. They don't. Pomade, clay, paste, and wax each behave differently, and using the wrong one for your hair type means fighting your hair every morning instead of working with it. The differences aren't complicated once you break them down by two variables: hold and finish.
Pomade sits at the high-shine end of the spectrum. It gives your hair a slick, polished look and stays pliable - meaning you can rework it through the day. It's best for straight or wavy hair worn in classic styles where you want some gloss: a side part, a slicked-back look, anything with visible comb lines. The trade-off is that it can look greasy on fine hair and makes volume harder to hold on thicker hair.
Clay is the opposite in finish - fully matte - and usually the strongest in hold. It adds texture and volume, works well for thicker or coarser hair, and gives natural-looking structure without any shine. It's the product most guys with short textured cuts should probably be using. The key is to work it through warm, slightly damp hair rather than dry hair, which helps it distribute evenly.
Paste sits in the middle of both axes: medium hold, low-to-medium shine, flexible feel. It's the most forgiving product to use and the easiest to learn with. If someone tells you they don't know what they're doing with product yet, paste is usually the right first call.
Wax is more about separation and definition than overall hold. It gives individual pieces of hair movement and texture - useful for short crops, disconnected cuts, or anything where you want the hair to look deliberately piece-y rather than uniform.
On volume: most men use two to three times more product than necessary. A dime-sized amount is almost always enough for short to medium-length hair. Start small, work it between your palms first, and build from there. More product doesn't mean more hold - it usually just means a heavier, flatter result.
Get the cut right first and the product will have something to work with.