[pvg]

No, 'uniform' refers to the distribution, which need not be uniform, e.g.

https://numpy.org/doc/stable/reference/random/generated/nump...

Or in god's own words (TAOCP section 3.4):

Applications of random numbers often call for other kinds of distributions, however; for example, if we want to make a random choice from among k alternatives, we want a random integer between 1 and k. If some simulation process calls for a random waiting time between occurrences of independent events, a random number with the exponential distribution is desired. Sometimes we don't even want random numbers — we want a random permutation (a random arrangement of n objects) or a random combination (a random choice of k objects from a collection of n).

In principle, any of these other random quantities can be obtained from the uniform deviates U0, U1, U2, ...; people have devised a number of important "random tricks" for the efficient transformation of uniform deviates. A study of these techniques also gives us insight into the proper use of random numbers in any Monte Carlo application.

[jerf]

"All distributions are uniform" is one of the two cardinal crimes of a school level of statistics understanding, the other being "all probabilities are independent".