The ‘testing vs checking’ topic has been in discussion for many years in the software testing community. Two very vocal participants are James Bach and Michael Bolton.
“…we distinguish between aspects of the testing process that machines can do versus those that only skilled humans can do. We have done this linguistically by adapting the ordinary English word “checking” to refer to what tools can do.”
“One common problem in our industry is that checking is confused with testing.”
~ James Bach & Michael Bolton 
The issue I have with the checking vs testing topic is that it is dogmatic in implying that almost everyone around the world confuses checking with testing. Apparently unit testing is actually unit checking, the test pyramid is a check pyramid, test driven development is check driven development, and there is no such thing as automated testing, only automated fact checking.
“The “testing pyramid” is a simple heuristic that has little to do with testing. It’s called the testing pyramid because whomever created it probably confuses testing with checking. That’s a very common problem and we as an industry should clean up our language.”
~ James Bach 
We don’t need to clean up our language: we need to adapt, invent new language and move on.
The meaning of words aren’t static. ‘Literally’ originally meant in a literal way or sense but many people now use it to stress a point. ‘Awful’ used to mean inspiring wonder but now has strong negative connotations. Testing now means checking. Checking now means testing.
So perhaps instead of accusing everyone of confusing ‘testing’ and ‘checking’, we move on, accept people call checking ‘testing’, and come up with another term to describe the value added human stuff we do on projects: you know, the questioning, studying, exploring, evaluating etc.
It’ll be much easier to educate everyone on some new terminology for
pure human testing exploratory testing based on intuition, instead of trying to get them to split their current view of testing in half and admit confusion on their behalf.
 Testing and Checking Refined: James Bach – 26 March 2013
 On Testing and Checking Refined: Michael Bolton – 29 March 2013
 Disruptive Testing Part 1: James Bach – 6 Jan 2014
 From abandon to nice… Words that have literally changed meaning through the years