The consistency of a purchased chemical rarely has anything to do with its purity or identity. If you've synthesized it, then it will form characteristic crystals, but we're buying processed products, and they are milled to whatever consistency the manufacturer chooses.
If you suspect that one of them isn't potassium sulfate, then there's no good reason to suppose that it's anything else in particular. There are a few relatively simple things you can try to identify it, but by and large you've just got mystery powder.
Things to try:
1. Flame test: You probably did this one in chemistry class. Dissolve a small amount of the salt in an alcohol/water mixture, then use a small loop of wire with a long handle (like a bubble wand, but with a tiny bubble blowing end) to scoop a bit out. Darken the room and hold it over a hot flame (blow torch or kitchen stove preferably, a lighter, candle, or match if you're really desperate) and look for colors in the flame. This is a less than ideal setup, and potassium flame tests are fairly weak, but if it contains potassium you should be able to see lavender in the flames. You may also get a whiff of sulfur at this point and solve the mystery entirely.
2. Selective precipitation:
Do you have any soluble calcium and/or magnesium salts (CaCl2, for hardness adjustments or as ice melt salt, for instance? Epsom salt?) If so, mix a solution of calcium salt with a solution of the K2SO4. If nothing happens, it's not sulfate or phosphate. Try a solution of magnesium salt. If nothing happens it's not phosphate. There are a billion other things it could be, but if we're limiting ourselves to sulfate/phosphate/nitrate, then that tells you which is which.
Potassium nitrate is a strong oxidizer. If you have common sense and a safe place to do this, mix equal amounts of sugar and mystery salt, place it outside on a non-flammable surface, and light it on fire with a blowtorch. (You can use matches or a lighter, but it's more difficult to get started and you risk burnt fingers.) If it's KNO3, it will burn completely and brightly, producing lots of white smoke. If it's sulfate or phosphate, you'll look ridiculous in your driveway.