Is the term 'interpretation' in quantum mechanics the same as the term 'interpretation' in probability?

There are similarities and differences.

In probability, both interpretations give the same $P(A)$ for an event. But the interpretation of the even is the same: the event is absolute, i.e. it really happened.

In quantum mechanics, all interpretations give the same probabilities for a measurement outcome but the interpretation of the measurement outcome itself may vary.

In collapse theories, the measurement outcome is absolute and really happens, but causality is violated.

In many worlds, there is no single measurement outcome. The world becomes a superposition two worlds, each with its own outcome, and the observer in each world seeing (subjectively) a single outcome.

In Quantum Bayesianism, the probabilities and the measurement outcomes are completely subjective. This is actually a reformulation of probability theory where probabilities can interfere like waves. (This is because, in QM, the probability for a measurement $a$ is given by the square of the probability amplitude, $p=|\psi(a)|^2$. Since $\psi$ is, in general, a complex number, we can get interference between different classical processes by taking superpositions $\psi = \psi_1+\psi_2$.)

A recent paper (referred to in the following article) makes some of these ideas rigorous: https://www.sciencemag.org/news/2020/08/quantum-paradox-points-shaky-foundations-reality

But the point here is that the different interpretations of QM predict a different final state of the world and of the system after a measurement is made. However, how that measurement outcome is perceived by the observer making the measurement will be the same in all interpretations. So there are no observable differences between the different interpretations, only inobservable differences.