This page is a work in progress.  I add words as needed based on the posts I publish.

Mode of Control The way in which a signal responds to real time traffic demand.  On one extreme, a fixed-time intersection might have no real-time inputs (i.e. entirely pre-timed), and on the other extreme, a fully-actuated intersection will base all phases and durations based on real-time demand.  The common middle ground is a semi-actuated intersection, where all but one of the phases are called and/or extended based on real-time demand.  The City of Toronto covers the common examples here.

Leading left turn phase: The left turn precedes the corresponding through movement.

Lagging left turn phase: The left turn follows the corresponding through movement.

Permissive turn: Drivers wait for a gap in opposing traffic to proceed.

Protected-permissive turn: Drivers may proceed on a green arrow with priority, but can also make a permissive turn at other times in the cycle.
Prot-Perm display

Fully-protected turn: Drivers may only proceed when they have green arrow.  Typically there’s a separate Left Turn Signal, but this is not necessarily the case.
Protected Display or SplitPhasing Display