What do you call numbers such as $100, 200, 500, 1000, 10000, 50000$ as opposed to $370, 14, 4500, 59000$

The first category is known as the 1-2-5 series, and it is an example of a system of preferred numbers. As the name implies, there is nothing mathematically distinctive about such numbers; humans just prefer them.

The OEIS calls your first set a "Hyperinflation sequence for banknotes", though there have been many coins and banknotes with different denominations around the world, such as a $1935$ Canadian $\$25$ note.

Mathematically they are the numbers generated by $$\frac{1+2 x+5 x^2}{1-10 x^3}.$$

People have counted with other patterns, notably the Babylonian sexagesimal system which we still use for minutes and seconds and so often think of $15$ and $30$ as round in some contexts.

I believe the most easily understood term for them is numbers with one significant figure.

Preemptive argument against pedantic people:

While it is true that "with one significant figure" can be used to describe a value and does not serve the asker's purpose in that case, it can also be used to refer to number and when it does, it does serve the asker's purpose. How clear one must be to ensure that everyone knows you are referring to numbers, not values, depends on the context the phrase is used in.

Secondly, one might say you need to specify the number system when speaking of significant figures, however, if you don't, in most contexts it can be assumed you are talking about decimal numbers.