Are the assertions "$2 + 2$ equals $4$" and "$2 +2$ is $4$" identical Are the assertions "$2 + 2$ equals $4$" and "$2 +2$ is $4$" identical? Or is this a linguistic, psychological or murky philosophical thing rather than a mathematical thing
I think that we should first ask "In what language are these assertions made?". The assertion does not belong to the mathematical language, where it should be written "2+2=4" or more basically, using the language of the Peano axioms: "$s(s(0))+s(s(0))=s(s(s(s(0))))$". If it's in the English language, then one must ask if "equals" and "is" mean the same thing all the time or only when they are used between two numbers or numeric expression.
Clearly, 2+2 is not identical to 4. 2+2 is the sum of two twos but 4 is a single number. What we mean by either way of saying it, is that 2+2 is quantitatively equivalent to 4. And I wish we would use the identity symbol and reserve the equals sign for conditional quantitative equivalence.

This also applies to 0.9999... is quantitatively equivalent to 1. They are obviously not identical. Mathematics should not rule out common sense.