Does an electric motor benefit by being given a rest?
Will the following two scenarios give different results on the
wear/safety of a consumer-grade electric motor:

Yes, but what difference there will be is dependent on too many variables to say which of your two scenarios will result in more or less 'wear/safety', or whether the difference will be significant. For example:-

A has 20 times more starts and stops than B, which will increase brush wear and commutator erosion in a brushed motor. But 20 starts and stops isn't many, so the difference may not be significant.

B runs the motor for 20 times as long without a cool-down period. Depending on the time taken to reach equilibrium temperature, B could expose the motor to higher temperatures for longer, which may degrade various parts (insulation, bearings, magnets...) more.

On the other hand, running at a constant temperature reduces stresses caused by temperature changes, and if the motor is operated in a high humidity environment then running continuously may protect it from corrosion and insulation breakdown.