The answer is simple. Frasier Crane was was played by Kelsey Grammer not our beloved Fred Thompson.
Side by side photos seem to clear things up:
Grammer looks a good 40 years younger than Thompson. However, without Grammer's stage make up, the difference is more subtle. (Click the photo above to see a comparison to Grammer without make up).
No one would confuse the two if they heard them speak. Kelsey Grammar sounds like an over-enunciating East Coast patrician while Fred sounds like the narrator of those Disney nature movies from the 60s who would tell us what we could clearly see for ourselves like "The bear hibernates in the winter," or "Ducks fart underwater then swim away before the toxic fumes can reach the surface."
Another reason the two are mistaken for each other is their young, blond wives.
A close inspection of this photo reveals a key difference: Fred Thompson's wife is young enough to be Kelsey Grammer's wife's daughter.
UPDATE: The babe-in-arms race continues--Grammer traded in the one pictured above for a much younger model.
In the final analysis, it really doesn't matter if the two are confused with each other. But men enunciate clearly and are highly capable at reading off a teleprompter. Therefore, either would be equally well-qualified to be the GOP nominee for president.