Generational is overused.
Crosby, Ovechkin, and McDavid are the only current generational players. Some people might dispute Ovechkin, but when a player in the kind of scoring environment Ovechkin has played his career through has even a slim chance of being the most productive goal scorer of all time, that's a generational player. It's something we might not see again for decades. McDavid has already won two Art Ross trophies, he won the Hart trophy in his second year. It took Kucherov having a remarkable season on a stacked Tampa team for McDavid to lose out on a third straight Art Ross trophy. It also might be arguable that where he was trending as an 18 year old prior to getting hurt, that he could have overtaken Jamie Benn to win the Art Ross that year. I'd say he's generational because there are so few examples in the entire modern history of the league of players coming into the league at 18 and dominating production wise like McDavid has.
Previous to that, guys like Orr, Lemieux, Gretzky, and Hasek probably take the mantle. I'm missing a bunch because I am the farthest thing from a hockey historian, but those are the obvious guys where their performance was so far above everybody else at the time.
A franchise player is a player who drives things and wins games at a top level. Someone that can be built around as the central piece on a team. Typically, they make guys they play with much better. The big distinction between franchise and generational is that generational players are accomplishing things individually that haven't and won't be seen in decades. Nathan MacKinnon is a top level franchise player. The problem with franchise vs elite is that defensive ability is much more difficult to quantify. There are players like Bergeron, O'Reilly, and Stone that most people would only call "elite" players because in their average seasons they are never going to touch the most productive guys in the league. Their hockey sense and defensive abilities are so off the charts, and with a guy like Mark Stone he clearly drives his line and makes guys around him better. So it makes me wonder if he's a "franchise" winger.