What does the term "differential" in "differential privacy" mean?
The term "differential" was proposed by Mike Schroeder, to characterize the guarantee as being a relationship between distributions with and without any input record. At the time most papers simply defined "(x,y,z)-privacy as ..." and the work felt of a sufficiently different character (both weaker and stronger than prior work) to call out the distinction.

Other adjectives that were discarded were "incremental privacy" and "marginal privacy", for retrospectively obvious reasons.

The name stuck in part due to the analogy to differential cryptanalysis.
Yes, per Ted's answer, which is exactly correct.