For levels where you get a new mystic arcanum, the warlock leveling table also shows that you get one more spell known. Are they the same spell, or is the spell you get from mystic arcanum a different thing altogether?
I looked at Reddit for answers, and they had one claiming that they are different things, but the rationale seemed more opinion-based than RAW based.
Per the Player's Handbook:
The Spells Known column of the Warlock table shows when you learn more warlock spells of your choice of 1st level and higher. A spell you choose must be of a level no higher than what’s shown in the table's Slot Level column for your level.
The Slot Level column never increases above "5th", so a warlock can never know a warlock spell of 6th level or higher.
Therefore the Mystic Arcanum spells must be known separately from the warlock's Pact Magic spells.
No, the warlock's Pact Magic feature is a completely separate feature from the Mystic Arcanum feature, and each independently describes how you get spells without relying on or referring to the other. Pact Magic says you get another spell known at e.g. 11th level, so you do, period. The Mystic Arcanum feature, separately, gives you access to a new spell that you can use with the Mystic Arcanum feature.
If that reasoning is not convincing, here's a bit of circumstantial evidence underlining the necessary separation of the two features: Notice that the spells you gain access to with Pact Magic and Mystic Arcanum cannot be the same due to incompatible spell levels! All Mystic Arcanum spells you gain are of a level (6th and up) that is inaccessible to your Pact Magic, which tops out at 5th-level spells. For example, at 11th level, you gain a new spell known of maximum 5th-level via Pact Magic, and a 6th-level Mystic Arcanum spell. These cannot be the same since they are different spell levels.
