Incomplete TST

An incomplete TST is a TST where at least one of the rows isn't fully filled. For example, STSD is a particular case of incomplete TST.

TST chaining
When the missing mino is three cells away from the T-slot, one can follow up an incomplete TST with another TST.

It is sometimes possible to do an imperial cross or just a TSD instead of the TST.

Switchback
Switchback is a particular case of TST chaining which results in a C-spin instead of a TST.

Situational setups
A few more examples can be found on this fumen.

Ventilator
Ventilator is an incomplete TST with the missing mino on the second row next to the T slot. As it is sometimes used by the bot Cold Clear, it is called CC砲 (CC Cannon) in the japanese community.

This setup often leaves unclean residue, but it is sometimes possible to incorporate it in another T-spin setup.

It is also possible to follow up ventilator with another TST or TST chaining.