Recipe for butter chicken: roasted pieces of tandoori chicken in a tomatoey butter based sauce.
Recipe for chicken tikka masala: roasted pieces of tandoori chicken in a tomatoey cream based sauce.
As is often the case with cultural appropriation, the real innovation by the appropriator was the marketing. In my view, this is what probably happened: multiple restaurants found the fake origin story a profitable and interesting marketing tool and judging by how popular indian food is in the UK today, it obviously worked.