John Mueller from Google said on Twitter "counting links on the web correctly is technically impossible, and everyone just makes different approximations & assumptions." This is in response to third-party link tools not matching up or looking inaccurate.

As you know, the web and web pages across the web are not perfect. So analyzing something that is not perfect, have markup issues, and bugs, can be challenging, to say the least. Google does it, Bing does it, search engines do it and third-party tools that analyze the search results or web pages do it as well.

What John is saying is that this is a hard problem to solve, each company that tries has to make their own "approximations & assumptions" and thus, there is no correct answer to measuring links on the web.

Here are those tweets:

I'll go out on a limb and say counting links on the web correctly is technically impossible, and everyone just makes different approximations & assumptions. — 🍌 John 🍌 (@JohnMu) September 12, 2019

Russ from Moz responded in a similar fashion:

Agreed. Which is why when presenting data we should be as clear as possible about how it is collected, counted, what assumptions are made, etc. — Russ Jones (@rjonesx) September 12, 2019

Forum discussion at Twitter.