the main distinction i like to make is:

your FDEs shape your product strategy, and should be considered R&D. after making sure a customer deployment is successful (by any means necessary btw, even if it means building new systems outside of the product), the crucial next step is to drive the product improvement with PMs and core software engineers after contact with reality. this was a pretty radical idea from palantir in the era of saas

if you only do step 1 you're basically just solutions engineers / mckinsey, and if you only do step 2 with no customer learning to your product you don't improve your platform for all the other customers. the pain becomes the moat

There's a reason why this echelon of companies comp FDEs much, much more than services businesses is because you're trying to find engineering + product + customer facing in one (knew people making 200k+ 5 years ago as new grad FDEs, and the same flavour at the labs is 500k+ easy)

that being said the role has evolved a lot over the years, and depending on the company it could be indistinguishable from solutions eng, or sales eng, or even dev rel.