Ecto Association vs Foreign Key Constraints

I’m having trouble understanding the difference between cast_assoc, assoc_constraint and foreign_key_constraint in a changeset. More specifically, I don’t seem to understand when you should build your associations explicitly (by putting foreign keys) versus letting Ecto build them with associations.

I have a schema like this:

schema "institution_codes" do # InstitutionCode
  field :code, :string
  belongs_to :source, Source
  belongs_to :institution, Institution
end

def changeset(struct, params \\ %{}) do
  struct
  |> cast(params, [:code])
  |> cast_assoc, assoc_constraint or foreign_key_constraint?
end

…and in my migration:

create table(:institution_codes) do
  add :code, :string
  add :source_id, references(:sources)
  add :institution_id, references(:institutions)
end
create unique_index(:institution_codes, [:source_id, :institution_id], 
                     name: :institution_codes_index)

If I want to insert a record into institution_codes, should I be looking up the foreign keys of the Source and Institution schema and explicitly putting them in source_id and institution_id in my InstitutionCode schema params then inserting the record, or putting associations?

The unique constraint on InstitutionCode doesn’t seem to work when putting associations. When I try to insert the record I get errors in my changeset that there are uniqueness violations in the Source and Institution schemas because Ecto is trying to insert the associations. I want it to put the keys of the associations as foreign keys in the InstitutionCode record, not insert the associations themselves.

I feel like I have a fundamental misunderstanding of how these should be used.