Theoretically, no, they're not. Cogs (and the spacers) from different "speed" cassettes are different thicknesses.

However, you can sometimes swap one cog of the "wrong" thickness successfully. I substituted a 26T 8-speed cog for a 25T 9-speed cog in a 9-speed cassette and it fit and shifts fine. However, that's only one substitution. Generally you can't mix-and-match at will.

In your case, it sounds like you want to put an 8-speed 16T cog into a 10-speed cassette and I don't think that will work. The 8-speed cog is thicker and the 10-speed chain may have problems with fitting over the teeth properly. Try it but don't expect much.