Titans/Oilers are one and the same. Sometimes teams will separate from their old city such as the Baltimore Ravens do not hold claim to their past in Cleveland, and those records remained for the new Browns franchise to claim.
The sentiment is nice, and if you are only going by tenure in one city then it's true, but IMO there really isn't a separation of Houston/Nashville with the Titans as much as other franchises that have moved due to the fact that Bud Adams remains such a big Houston guy, the fact that Houston was awarded a new team with a different name and look, and the team still has holdovers from Houston up until this coming summer (with Fisher and Underwood). Plus Wycheck and Bishop on the radio daily. Also the fact that the team played as the Oilers in Memphis and Nashville, so the situation just doesn't lend itself to considering the Houston Oilers and Tennessee Titans as different entities. Maybe it will feel different in 10-20 years, but the Oiler vibe is still felt with the Titans.
So if a guy coached the Chicago Cardinals and the Phoenix Cardinals, that would be the same team? Just like the Rochester Royals and Sacramento Kings.
I guess you mean Arizona Cardinals.......but yes. Chicago Cardinals are what the Arizona Cardinals used to be. It's all the same. The Titans were not an expansion team. Their history goes all the way back to the Houston Oilers.