Measuring qubits vs measuring operators

Question

I'm having trouble unifying these two ideas. When I read examples using, say, qiskit, it's typical to measure a qubit, so that to find the probability of measuring a state $|\psi \rangle$ in the state $|x\rangle$ is $p(|x \rangle) = (\langle x | \psi \rangle)^2$.

But when I read quantum computing textbooks, they usually refer to some observable that is getting measured. So what is the operator that gets measured when we "measure a qubit"? Is it the identity operator or something?

Answer 1

"Measure qubit $q$" = "Measure the $Z_q$ operator"

More generally, "measure the operator $P$" can be operationalized as "apply a sequence operations which sends $P \rightarrow Z_q$ then measure qubit $q$ then undo the operations to restore $Z_q \rightarrow P$.