HIIT describes a way of organizing intensity. Functional training describes a broader training approach. They can overlap, but they are not the same thing.
HIIT
High-intensity interval training alternates hard work with periods of lower effort or rest. It can be useful for conditioning when programmed appropriately.
Functional training
Functional training can include strength, carries, hinges, squats, pushes, pulls, locomotion, mobility, stability and conditioning. A functional session can be intense, but intensity is not the only purpose.
How LTE uses the terms
LTE’s functional training combines strength and conditioning with mobility, stability and movement quality, rather than making every session a race against the clock.