In my previous airline yes, we only had the 752, 762 and 763 in the fleet and so all pilots were qualified to fly all three "types".
The type rating is initially 757-only, with the cross-qualification for the 767 (making it a 757/767 rating) permitted by successfully completing a differences course.
There is no currency requirement for flying the different types, we keep the CAA happy by simply doing alternate sim checks (757 then 767, etc....)
In theory you could fly the 757 for say 5 or 6 years, then step into the 767 and be perfectly legal to fly it. In practice this is extremely unlikely to happen. Even BY
pilots at 757-only bases will take a 767 roundtrip across the pond at least once every year to keep their ETOPS currency, for example.
In my present airline all pilots are 733 and 73G rated (differences course again permits the latter). The common type rating means exactly the same applies, alternate sim checks and we're good on both (despite the fact that some bases are practically all 733 and others 73G).
When the Airbus arrives it will all go to pot
I used to love the smell of Jet-A in the morning...