I know a floor prevents a player from dropping below a certain rating. For example, if a player reaches 2200, then he or she can never drop below 1800, no matter how many games are lost. I'm not sure if those are the actualy numbers, but you get the idea. This is to prevent sandbagging - a stong player losing games on purpose to get into a lower section of a tournament, where he or she is more likely to win the prize money.
I've never heard of a norm title. Norms (GM norm, IM norm) are given when a player does exceptionally strong in a tournament. A player has to reach a certain rating and get a certain number of norms to reach IM/GM level. I don't know if there are norms for CM/NM/FM.
USCF issues norm titles for 1200 1400 etc. but at the same time issues floors. What is the difference?