I think there is a major strategy difference between the two.
In limit, you will likely have many many more multi-way pots. This creates great pot
odds for the players, and it is almost impossible to get players to fold. If you can't get your opponents to fold, then a huge part of the game goes away. Because there are more players in the hand, the winning
hands at showdown will generally be much bigger - you will generally need straights and flushes to beat multiple players.
In no-limit, of course, the opposite is true. Now, our bets can be sized to mean something. You can play to get an opponent to fold. There are less multi-way pots, because our
pot odds aren't as good. We may see very few showdowns, thereby getting very few clues as to what our opponents are actually playing.
The only commonality is that the rules of the game are the same and the odds and equities remain constant. There is very little commonality for strategy. I would recommend you pick up a no-limit holdem strategy book if you plan on playing no-limit. Abandoning the limit strategy book ASAP would be good for you.
Good luck!