Same height, two floors
This is the profile for a doorway between two rooms with floors that finish level with each other, whether they are the same material or not. Neither floor is higher, so nothing has to ramp, and the T simply covers the join.
If one floor is higher than the other, this is the wrong profile and an end cap or a reducer is what the condition needs. Which of the two situations a doorway actually has is settled on site, not on the plan.
The other reason for a T-molding
Long runs of floating floor are laid with breaks in them, because a floor that runs uninterrupted past a certain length has nowhere to absorb its own movement. A T molding is what covers that break in the middle of an open area.
It is the reason a T sometimes appears where there is no doorway at all, which looks arbitrary until you know what it is doing. Where those breaks fall depends on the shape of the floor and is decided in the room.
The T-molding stem
The stem of the T drops into the gap between the two floors and the arms rest over the surfaces either side of it, without being fastened to them.
That arrangement is deliberate: both floors keep moving underneath, and the molding stays put. It is also why a T has to suit the width of the gap and the thickness of the floors, which is why trim is bought against a specific floor.
T-molding width
T moldings vary in how wide their arms are, and the wider ones cover more of each floor either side of the join.
That matters where the two floors were not cut to a tidy line, which in a doorway is common. A wider profile forgives more; a narrow one reads more neatly where the cut is good.
Matching two different floors
Where the two floors are different, the T can only match one of them. The usual answer is to match the more visible floor, or the one in the larger room, and let the join read as a deliberate line.
The flooring trim page covers the other profiles a floor needs, and the LVT moldings range gathers the vinyl versions.