Generator/Alternatives/Google Authenticator
Google Authenticator and this page compute the same six digits from the same secret, because both implement RFC 6238. The difference is not the algorithm — it is where the key lives and what happens when the phone is not in your hand.
Gen2FA is not a replacement for Google Authenticator. It holds nothing you have not pasted in, it lives in one browser, and anything you save here is stored in readable form. Keep an authenticator app enrolled and keep your recovery codes. This is the route in when the app is out of reach.