Shimano, Mineral, LHM, Audi PS Fluid, OM15 – all the same basically, and compatible.
Dot anything is non-mineral hydraulic oil. Can be mixed, but why would you use 4 if you could use 5.1? (BTW, Dot 4 boils at 155C wet and 230C dry, Dot 5.1 boils at 191C wet, 270C dry – That’s the DOT spec, so if you find a brand of ‘DOT 5.1’ which boils lower, it ain’t 5.1)
Dot stuff is pretty horrible, mineral stuff is much more pleasant. Both types will get past the other one’s seals, so wrong fluid = lots of leaks and new seals all round. Not good.