The short answer
A posting schedule is the timing: which days and times content goes out. A content calendar is the broader plan: what content goes out, tied to which pillar or goal, on what schedule. A posting schedule is one component of a full content calendar, not a substitute for it.
Why the distinction matters
A posting schedule alone answers "when," but says nothing about whether the content itself is planned or worth publishing. A business can have a perfectly consistent posting schedule and still be scrambling for what to post each time, which is the problem a content calendar is meant to solve.
A calendar without a schedule is just as incomplete
A list of planned content ideas with no assigned publishing rhythm tends to drift, since there is no forcing function pushing any of it out the door. The two work together: the calendar decides what and why, the schedule decides when.