What is the difference between pulsatile current and interrupted pulses as a description of current modulation?

They are the same thing. A single pulse is defined as an isolated electrical event separated by a brief, finite period of time from the next event. Pulsed current (Also Known As [AKA] pulsatile or interrupted current) is the unidirectional or bidirectional flow of charged particles that periodically cease for a brief, finite period of time. It is also referred to as interrupted Direct Current (DC) or interrupted Alternating Current (AC).

Reference 1: Robinson A J, Snyder-Mackler L. Clinical Electrophysiology; Electrotherapy and Electrophysiologic Testing. Lipincott Williams & Wilkins. 3rd Edition. Pg 13.