Is there such a system in London between Underground and National Rail?
I believe there is such a system between National Rail and the Tyne and Wear Metro between Newcastle and Sunderland.
It depends, and it is complicated.
There is some inter-availability for some tickets- usually singles, returns, and some point-to-point season tickets. Examples include on NR and LU between, for instance, Queens Park and Harrow and Wealdstone or between King Cross, Highbury and Islington, and Finsbury Park, or on NR and Metro between, for instance, Newcastle Central, Heworth, and Sunderland.
Otherwise the single/return/point-to-point season ticket prices don't always align. Between, say, Richmond and Waterloo the price you pay for a single ticket depends on whether you go by train or by LU.
TfL travelcards (and contactless caps), though, are mostly zonal, so then you pay for the zones you go through. This is the same price whether you travel by train or tube. It is similar in Tyne and Wear, which is also zonal for the PTE season ticket and their ticket can (depending on zones) include train, ferry, bus and Metro.
Greater Manchester doesn't have a zonal season ticket which includes all of the trains, trams, and buses.