It's true. It doesn't have a name because it's not a thing. As a violin teacher, if someone did that I would stop them and say,"You're not doing vibrato correctly." I get what you're asking for, a name for the incorrect thing, but there is no name for it since it's simply being done incorrectly. Like, if you filled out the paperwork correctly, you are now registered to vote. If you don't fill it out correctly, there's no word for that except "you improperly registered to vote". The end result of this incorrect, unnamed action is that you can't vote. As in the case of vibrato. If you do it wrong, you won't get the right sound effect.
As to your question of isn't it all the same because the effect is the same - the answer is no. The sound is not the same. When done in slow-motion the sound does seem similar because as the finger is pressing down the string it is bending it down; same on lifting it up (as part of that incorrect pulsing action). However, speed it up and you will at once see that the vibration of the string is lost, which is where all of the sound is found - in a constantly vibrating string. In order for a sound on the violin to remain clear sounding, the string must keep vibrating. If inhibited, by either a crooked bow, a sliding (drifting) bow or in this case, a sudden change from held-down finger to half held-down finger (which changes the vibration tremendously), the effect is a scratchy, unclear sound. Keep the finger down, or keep it floating on top as in harmonics and you are golden. Switch it too suddenly and you've gone and messed up your smooth vibration. Vibrato doesn't mess with the vibration of the string.
If a student forced me to call it something, I would call it a pulse, but I would hate to call it a name lest someone think it is a thing.