They are not "harder". They may feel a little different though, for sure. The difference is in the wound strings, different brands and kinds of strings will very the size of the wrap and core wires to get the tension and feel they want. It may take a few days to get used to but thats all.
Example, the wound strings of the Ernie Ball Cobalt sets have slightly lower tension due to a slightly thinner core wire but the wrap wire is a little larger to achieve the same string gauge. For the first few days it felt "rougher" on my fingers because the windings are slightly bigger. By day three I didn't think of it anymore.
Stainless strings don't wear frets out faster, at least not that you would notice. That question has been asked here a number of times over the years but the response is always "no", the difference in hardness in different strings is not of any real consequence. I think once someone on the internet mentioned the possibility people spend time checking for string wear and wrongly assume frets are wearing faster just because they are now looking when they never did before.
