Is there a difference between the initial appearance and the arraignment?

There is at the federal level. In a federal criminal case the federal rules of criminal procedure require a person making an arrest within the United States must take the defendant without unnecessary delay before a magistrate judge or before a state or local judicial officer. This must take place very soon after the arrest. The arraignment then takes place later.

Federal Requirements at Arraignment: Federal Rule of Criminal Procedure 10(a) states the following:

(a) In General.

An arraignment must be conducted in open court and must consist of:

(1) ensuring that the defendant has a copy of the indictment or information;

(2) reading the indictment or information to the defendant or stating to the defendant the substance of the charge; and then

(3) asking the defendant to plead to the indictment or information.