Tetrad basis: a doubt on "Comoving" and "Static" tetrads

In the awesome paper $[1]$, Müller then gives us a plethora of spacetimes and their basic geometrical objects like the form of the line element, Christoffel symbols, Krestchmann scalars and so on. Futhermore, we can see that in the paper Müller also gives us tetrads.

So, I would like to ask what is a Static Local Tetrad and Comoving Local Tetrad?

$$* * *$$

$[1]$ MÜLLER.T; Catalogue of Spacetimes; arXiv:0904.4184