first noticed that my X is listed by my insurance company as a performance model
Probably just a [costly] error from your insurance company.
Tesla renamed its "Performance" vehicles to Plaid when they changed to the Palladium platform (like the one you bought), so technically Tesla is no longer selling any "Performance" branded models since mid 2021.
Do both models have spoilers?
All Model X's have a spoiler since they came out in late 2015 as 2016 model years. Back then, there was an "Active Spoiler" option which changed height depending on the speed and tucked away when the vehicle was parked, but Tesla took it away as it was a massive pain to fix when grime and dust collected in the motor hinges and stopped working, so now we just get the fix spoiler for each and every Model X.
Plaid's have 3 motors as opposed to the 2 on the Long Range. (By the way, there's no longer a Long Range version of the S and X models, there's just the Plaid and the "Model S/X").
The easiest way to tell if you have a Plaid Model X, is by opening the
Additional vehicle information pop-up window in your
Controls -> Software menu screen. If it's a Plaid (which I don't think is the case with your Model X, as from your photo, it doesn't seem to have the contrast stitching on the seats), it should mention that the rear motor is a:
Dual permanent magnet:
this could affect your insurance rates
As
@Les236 mentioned, you should get this sorted out with your insurance company, as Plaid's get a higher insurance rate than the regular non-Plaid Model X.