Cancels in DmC has a lot less usage in combat than movement. Although, there is SC application that is similar to DMC3's Weapon Switching.
Training mode identifies these specific cancels as Quick. Meaning, this is Quick Trinity Smash
Some moves that are done out of Rapid Slash are its own animation despite being the same move.
Since DMC4, JC became part of the upgrade shop and it costs 1 ability point to obtain. This is one of the main aspects for Dante's run. Because, some of his skips involves around doing Demon Pull loops to reach at certain platforms. Additionally, he could utilize moves like Stomp to deal more damage that depends on the height.
DmC JC window is more open than it's previous title which gives the player so much space to cancel instead of doing certain rhythm.
Angel Boost is an important tool for both characters. Dante acquires this in Mission 3 while Vergil already has it available from the start. Though, there are distinct difference on how they cancel and move:
Definitive Edition Angel Evades
Vergil's Plink Dash with Atomic cancels