Nitpicking your nitpick, the difference is whether the random sampling is with replacement or without replacement. Wikipedia's definition of "simple random sample" defines it to include both ways:

[S]ampling is typically done "without replacement", i.e., one deliberately avoids choosing any member of the population more than once. Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement.

Ref: https://en.wikipedia.org/wiki/Simple_random_sample