When people use the term “bridge deal” in the NHL, it is because the teams have a lot of control of young players and players cannot become unrestricted free agents until they are 27 or have 7 years in the league.
Teams have to decide how be use that control.
With a guy like Fox, there was no question he was really good and the Rangers signed him to a long term deal (9.5 million x 7 years). The Rangers are happy because they locked him up through age 29-30, three years part when he could have been a free agent. Fox is happy because he makes a ton of money and will become a free agent when he is young enough ti get another good deal,
It is when you don’t know how good a player really is that the bridge deal comes in.
Next summer K’Andre will be 23 years old, four years from free agency. The Rangers have cap issues the next couple of summers so giving him a two to three year bridge deal would work for them, because he is still not a free agent at the end of it. Miller probably won’t love it because if he has to wait until he is 25-26 a ears old to get his first big contract, he probably won’t get a second because he will be too old at 32-33.
TLDR- a bridge deal is a short contract that uses up some of the years a team controls a player, but not all of them, so they can put off giving that player a long term deal for a while.