I asked my mom what a period cramp is and she said it’s different then like a cramp you would get from running.

Your mom is totally right, period cramps are definitely not like a leg cramp from running. Period cramps are a special kind of cramp that happens in your uterus. It's basically your uterus doing a little squeeze party to push out the lining it built up, because you didn't get pregnant this month. So it's like a mini workout for your uterus, which can feel crampy.