[shkkmo]

Counting is a subset of estimation, not a synonym.

If I estimated the number of quarters in a stack by weighing them, that would be different from estimating the number of quaters in a stack by counting them. Both methods of estimation have error bars.

The list you provide is of categories that don't have clear definitions. If you have a sufficiently clear definition for a category given your population, it has a precise count (though your counting methodologies will still be estimates.) If your definition is too fuzzy, then you don't actually have a countable set.

[throwaway290]

It's close enough to counting for the purposes of a magazine article like uuids are close enough to being unique for the purposes of programming.

[shkkmo]

The algorithm accuracy scales with the ratio of memory to set size so you don't actually know if it is "close enough" without an estimate of of the set size.

I think the headline is clickbaity and the article makes no effort to justify it's misuse of the wors 'counting'. The subheadline is far more accurate and doesn't use that many more words.