Well, you kinda got it right.
The original Senators moved to Minnesota after the 60 season and became the Twins for the 61 season.
The expansion Senators started in 61, and moved to Texas after the 71 season and played in 72 as the Texas Rangers.
So actually, this current version of the old Senators has not played in a World Series.
A Twins/Giants scenario would be what you are talking about.
