Record type access in profiles versus permission sets
Key Takeaway
A profile holds the default record type and page layouts, and it can assign either the Master record type or custom record types, never both. Permission sets and permission set groups can only add custom record types.
A record type assignment controls which record types a user can use when creating or editing records. For example, a user might get both Hardware and Software record types on opportunities. You can assign record types in profiles, permission sets, permission set groups, or a combination of these, but profiles and permission sets behave differently.
Record type assignments and viewing records
A record type assignment does not control which records a user can view, because users can view records of any record type, even ones not assigned to them.
For example, imagine a user who has the Hardware record type assigned but not the Software record type. That user can still view opportunities that have the Software record type.