Other than being based in Winnipeg, the current Jets have nothing to do with the previous NHL Jets.
There's nothing to dispute about that. However, the only thing that remains the same about any other team is the name. The players are constantly changing from year to year. Jean Beliveau and Guy Lafleur no longer play for the Canadiens so does that make it a different team now? The ownership of teams also changes as does management. An argument can always be made as to what constitutes a 'team'.
The opinions will always differ as some only want to point out that a team had relocated from point A to point B and that the history should follow. Others believe the team name and records should remain with the city where they occurred.
Obviously sports is a different animal as it relates to the business world. The identity of a city is often tied to the teams that play there. It cannot be compared to a restaurant changing its name or moving from one street to another. A sports team creates a passion not matched by any other type of business.
The example of the ex-girlfriend or ex-wife or the family dog running away from home is often given as an example of someone trying to pretend the replacement is the same as the original by using the same name. The example is flawed and insincere. To look at it from the other side, if your ex-wife moved in with her new guy and took your children with her, does that make him their new dad? If he adopts them and changes their last name to his, does that mean you're no longer their dad? Do all the memories you have of them when they were growing up belong to him now?
There is nothing wrong with fans wanting to maintain (or bring back) a team name that they identify with. It's the fans that make the team relevant not the other way around. The players come and go but the fans remain. Memories from events that occur in one locale cannot be transported to another.
We were the ones that watched Bobby Hull, Dale Hawerchuk and Teemu Selanne. We're also the ones watching Dustin Byfuglien, Mark Scheifele and Patrik Laine. To us they were, are and always will be our Winnipeg Jets.