There is a record type in Account that I can see while I do SOQL in records but when I go to setup > object > record type. I am not able to find any such record type. Where else can I find the record types for account? I can also see this record type in Profiles level, but not in Layout assignments. I have checked the API and UI name properly.
Do you have person accounts enabled? It's probably one of these. In your SOQL go SELECT Id, Name, RecordType.Name, IsPersonAccount FROM Account WHERE Id = ...
What's your UI? In Lightning you should see all types on Account page (/lightning/setup/ObjectManager/Account/RecordTypes/view). In Classic it's a separate menu: