[anyoan1]

Is there any method to determinate what iodine compound (potassium iodide/potassium iodate) is in salt?

I have one salt with potassium iodate (+anticaking agent) and another probably with iodide (+anticaking agent), but i'm not so sure about it.

Is there any cheap/easy method to check what compound is in the second salt?

[Hunter2]

Yes. Iodide can be oxidised to iodine. Also can be  precipitated as silver iodide.
Add some acid and peroxide. Then some starch. If it's blue you have iodide.
Iodate can be reduced by several reduce chemicals like ascorbic acid and then also determined as iodide.