I think it's two different things. When using it to equalize ears hands free, it's the tensor veli palatini (tvp) you're contracting to open the eustachian tube.
Of course, one might not be able to distinguish what muscles one is contracting, so it might be that most people actually tense both the tvp and the tympani at the same time, getting both the roaring sound from the tympani and the clicking sound from the tvp when the tubes open. Hence it's two different, but connected, things.
tensor tympani rumble = deep continuous rumbling sound you may hear when yawning
Eustachian tube clicking = a single slightly wet click you hear when you move your soft palate to block off your nasal cavity from your throat (via the tensor veli palatini muscle)
Of course, one might not be able to distinguish what muscles one is contracting, so it might be that most people actually tense both the tvp and the tympani at the same time, getting both the roaring sound from the tympani and the clicking sound from the tvp when the tubes open. Hence it's two different, but connected, things.