Thank you Tim and thank you Trouble. Yes, I was indeed referring to the "product key" I had forgotten it was called such. I called it serial number because I looked at the bottom of my laptop and all I see is "S/N" hence me calling it such (bought at Walmart). However doing a double-check and looking under my other laptop it actually does have such a sticker ( I wonder if Walmart has anything to do with its laptop not having it).
Anyhow, so it seems I can safely use my USB created via Microsoft on one laptop on the 2nd one as well (since yes, my laptops did come with Windows pre-installed). But perhaps I should add something else. Both laptops had WIndows 8.1 and not Win10. They were upgraded from 8.1 to 10 during the free year. I believe this shouldn't change anything, right?
A slight correction perhaps. One of the laptops (The Dell with the actual sticker at the bottom) was in fact given to me by my employer (the university where I teach) hence I assume that the licenses on it may be a group thing--but I can not say for certain anything precise regarding this.)