The total angle is how it’s specified.
So in the picture the spill is 80° and the beam looks like it’s 20°, but the spill comes directly from the LED, behaving more or less like a point source, shining through the opening of the bezel, but the beam comes from the reflector, which is a light wave front as wide as the reflector, so it would be like 10°
A TIR is like a normal reflector but with a tiny lens in the middle that focuses what would otherwise be the spill.
This eliminates the difference in color temperature between the middle and the perimeter of the bundle of light.
There is still some spill with a TIR, but much less than with a normal reflector.
Led Lenser TIR optics for example are quite good at tightly focussing what would normally be beam and spill, into 1 beam.
The lens in the middle is therefore relatively large compared to more common TIR optics.