My question concerns tenor guitar, tenor banjo and mandolin if you learn 1 can you basically play all 3.
Tenor guitars are normally tuned in fifths, just like those other instruments. They would all use the same 'picking pattern', so basically yes.
The difference is stylistic, which lies in the strumming or picking hand (usually right hand). The violin uses the same pattern too, but the right hand saws away with a bow.
I say, if you learn to play one, you will have an intuitive grasp for all of them… that gives you a big head start.