Assuming in a Postgres database, you have a table called party, which can have less than 5 well-defined party_types such as 'Person' or 'Organization'.
Would you store the party_type in the party table (e.g. party_type = 'Person') or normalize it (e.g. party.party_type = 1 and party_type(id, name) = (1, 'Person'))?
And why?
If you are implementing party-role-relationship model or part of it, having party_type as a separate entity is very important. You may have many more tables with foreign key to party_type (for instance, to limit applicability of certain roles to particular party type[s], or to enforce relationships between different types of parties, etc). Using check constraints in any form (including enums) in such cases would hide the logic and make maintenance harder .
I would use an enum type for that.
I always use a lookup table since your app may expand ("Organization" may become "Retail organization" once you add "Institutional organization" for example). A single location for the type name is great when you realize the type is slightly more specific or different than the original name would imply. Also, this is a great place to add values specific to the type like "CanHaveMultipleLogins" which VERY often get hard coded.
