There are actually three clauses which are broadly called the “emoluments clauses.”

The first attempts to prevent corruption and foreign influence, and any attempt to declare anyone “royalty.”

No Person holding any Office of Profit or Trust under
[the United States], shall, without the Consent of the
Congress, accept of any present, Emolument, Office, or
Title, of any kind whatever, from any King, Prince, or
foreign State.  ̶  (art. I, § 9, cl. 8)

The second colloquially referred to as the “domestic emoluments clause” attempts to forbid domestic bribery and preserve the president’s independence.

The President shall, at stated Times, receive for his
Services, a Compensation which shall neither be
encreased nor diminished during the Period for which he
shall have been elected, and he shall not receive within
that Period any other Emolument from the United
States, or any of them.  ̶  (art. I, § 9, cl. 8)

Note that “encreased” is the older spelling used in the document.

And the third referred to simply as the “ineligibility clause” prohibits multiple potential simultaneous conflicting roles.

No Senator or Representative shall, during the Time for which he
was elected, be appointed to any civil Office under the
Authority of the United States, which shall have been
created, or the Emoluments whereof shall have been
encreased during such time; and no Person holding any
Office under the United States, shall be a Member of
either House during his Continuance in Office. ̶  (art. I, § 6, cl. 2)