Whatever you call it, there is one and only one “primary key”/“primary index”, and that is the one for which:
1 - Primary key values are unique for each record
2 - Every instance MUST have a primary key value (that means no null values)
3 - No duplicates (for combinations of the fields, not each individual one)
I can’t speak for AX because I work with NAV. In NAV though, in the table designer, they are all called “keys”. When NAV runs on SQL Server, it creates an “index” for each “key”. For purposes of NAV, the word “key” really means “sort order”. On SQL Server, what that means is that the “primary key” is created as an “index” with a “primary key constraint”. Often people call this thing the “primary index”.
When you define an index as the “primary key”, that implies uniqueness, and it should in any relational DBMS. As soon as you put a checkmark by a “primary key” property, you should no longer be able to disable the “unique” property. Uniqueness is part of the definition for primary keys, so it should really be irrelevant.
In SQL Server you see those little key symbols by the fields that are part of the primary key, so that you can tell visually which fields are part of the primary key. Knowing what the primary key is of any table is probably one of the most important things to know when you are developing for a relational database.
It might be that you have a compound key that allows null values in individual fields. You should NOT be able to enter the same combination of fields (whether that includes null values or not) more than once. It shouldn’t though, because it is contrary to what is generally accepted, but I can see how technically “1,,2” is still a unique combination, or even “,,”. However, you should NOT be able to enter either combination more than once.
Now if AX has something else that they call “primary index”, and if that would mean something other than “primary key”, so if you can have one “primary index” as well as a different “primary key”, then I would say that is a dumbass name, and it would be very confusing [:D]