imo

solo staker = anyone who puts up 32 ETH and has full custody of their validator (may even run hardware elsewhere)

home staker = anyone who validates the network with hardware at home. includes DVT stakers and rocket pool operators

staker = anyone who stakes in any way (LST, custodied, whatever)

stake responsibly // be a kind human // slomad

Like building cool things. Collector. Crypto since 2013.

doubtful. any method i can imagine to allow home stakers to be identified or self-identify could be gamed by those not running their nodes at home. but that doesn't mean it's not worth putting thought into!

Would it ever be possible to prove the difference between a solo staker and home staker?

I also like "solo operator" as "operators who are a priori untrusted" (could be a "home" staker who uses AWS to run their node for instance)

This means home stakers satisfy all 3. HS FTW!

Agreed! 

And as a subset of Home Staker: 

Squad Staker = anyone who validates the network as a part of a Distributed Validator cluster