Right Foot In: On odd beats (i.e. on the 1 & 3) all dancers tap their right foot inside the circle. This is used at the beginning of the dance as well as to reestablish beat/organization when needed.
Swing Out (aka the Charleston) can be done with a left-leg ball-change (often used by leaders in paired dancing) or a right-leg ball-change (often used by follows in paired dancing). In solo dancing, there isn't a functional benefit to either version. Typically, everyone does the left-leg ball-change version in the Big Apple. However, there's no hard and fast rule.
Swing High, Swing Low:
This is a variation on the Swing Out aka Big Apple Swing aka Charleston Basic.
Pump Handle:
This is a variation on the Swing Out aka Big Apple Swing aka Charleston Basic.
Pump Handle:
This is a variation on the Swing Out aka Big Apple Swing aka Charleston Basic.
Truckin' Base:
Truckin' is a walking basic with a heel twist that evolved to emulate waiter-performers (prominently from the Cotton Club). As such, truckin' is often styled with one hand wagging a finger to emulate spinning a drink tray and the other arm folded in front of you to emulate carrying a hand towel. One variation, sometimes referred to as Harlem truckin' also involves a shoulder back lean.