As by definition Universe is collection of every thing in space. So if everything in space is inside universe then why we talk about parallel universes? Wouldn't they be inside the universe by definition? How does term Multiverse really have meaning does it implies we have many other collection of everything?
The multiverse, more broadly speaking, is of ancient origin. Heaven and hell were not of this world but in a different world altogether.
But of course the modern mania for the multiverse is not referring to this but to universes parallel to ours. There are several versions:
many worlds multiverse: this takes the evolution law of QM as axiomatic and dispenses with the collapse. It was originally formalised by Everett and championed by DeWitt amongst others.
general relativity multiverse: that the universe is much larger than our observable universe and perhaps infinite in extent.
string theory multiverse: one of the selling points of string theory was its uniqueness as a theory. However, it relies on a landscape of vacua which tunes the basic constants of our universe. This of course loses uniqueness as there is a choice of vacua which the theory doesn't single out. Some string theorists made this weakness a strength by declaring all possible universes actually exist.
Smolin's Multiverse: Smolin invoked a Darwinian selection principle amongst baby universes to select universes. In a sense, he is invoking the anthropic principle.
There are probably many others. The main criticism of multiverses is that they aren't scientific in the sense of being falsifiable in the Popperian sense. All the parallel universes listed above are causally disconnected from ours so there is no way of even finding them, never mind exploring them. Few advocates of multiverses care to tackle this critique, however one author of a book of many worlds multiverses did manage to say the notion is "extravagant". Indeed. What they are generally engaged in is not physics as understood by Galileo or Newton but metaphysics but such poor metaphysics gives metaphysics a bad name. Especially metaphysics that doesn't name itself as such but pretends to be physics ...
Sometimes these multiverses are spurious. For example, lattice QG in the early 2000s predicted a fractal-like structure of baby universes which might have prompted the invention of fractal ontology. However, the theorist Renate Loll pointed out that once these models actually used a Lorentizian metric as opposed to a Riemann metric the fractal structure disappeared. One might ask why did they dispense with a Lorentzian metric given that they were exploring quantum gravity and gravity means GR and GR as Einstein discovered it has a Lorentzian signature? The only reasonable answer is that calculations were easier in that framework ... never mind that in the light of what we know this is the wrong direction to take! The moral of this story is not to take the results of physicists on blind faith but to question them on what assumptions and approximations they used to come up with their theory ...
More broadly speaking, you are correct to identify the multiverse as simply the universe as the latter means all that there is. Likewise the atom meant something that was unbreakable but of course atoms break all the time. This is just part of language change. Language changes all the time. Much more often than inventing a new word, words change by stretching or contracting what they signify. Sometimes a new meaning stretches the word too far to be generally taken up. This is not what has happened to the world, "multiverse". It is an interesting question why such esoterica is part of everyday language now. Part of the answer, I suspect, is that people have always been interested in exploring what occurs beyond limits and what more stronger limit is that imposed by being of this universe? Another part of the answer is that publicity departments of universities weren't above hyping this esoterica to the public as they knew it would catch the publics attention. Its an easier sell than selling the next decimal point on a measurement ...
We coin words to describe things as we currently understand them to be. As we learn more, and realise our original word no longer fits, sometimes we keep the word and change the definition. The word 'atom' means 'indivisible', so the phrase 'splitting the atom' becomes oxymoronic in the same sort of way.
We originally defined 'universe' in the way you suggest - everything that exists in space and time. We built a model of what it looked like. Then later, we learned more, and realised that you could have several of these things we were calling 'the universe' existing in parallel. But like the word 'atom', the word 'universe' was already firmly attached to a particular picture. So we changed the definition instead and invented a new word for everything that now exists in our new, much bigger, and much less familiar picture. The familiar word is used for the familiar concept; the new word is used for the new concept.
The new definition of 'universe' has to be determined from usage, and it is not trivial to do so. It's now something like "everything that exists in a part of space and time that looks like the sort of classical universe we feel we experience". 'Causally-connected component' is wrong. In the 'Many Worlds' multiverse the branches are causally connected - they're just connected like a tree rather than a straight line. Several of the other 'multiverse' concepts (like the 'deeply-nested simulations' multiverse) have causal connections linking them, too.
To some degree, the dividing line is also associated with where things become metaphysical. The stuff we can never observe or test experimentally, even in principle, tends to get excluded from our picture of 'the universe'. Occam's razor can be wielded in two distinct ways - to objects, or to rules. Scientists look at the world of objects, try to devise the simplest possible 'rules' or 'laws' that they appear to obey, and then extrapolate the consequences of those rules. Sometimes the rules imply the existence of objects we cannot ever see or test, even in principle. But to exclude them, we have to invent a more complicated rule, to explain their absence. And because it is an area beyond the reach of experiment, we have no way to decide which of the many possible more complicated rules we should pick.
It was the same with the concept of 'infinity'. We cannot see the edge of the universe, it extends out of sight in all directions, so we have no way to discover the rules that determine its size, or what happens at the edge. The simplest solution is to determine rules that apply here where we can see, and extrapolate the consequences indefinitely beyond the range of our sight. We have no rule to describe or predict an edge, so we assume there isn't one - that's 'infinity'.
If we make up an arbitrary story to explain the presence of an edge, we find we have to keep moving it as we discover more. We started when we could see as far as the edge of the tribal territory. We expanded that to the edge of the trading network of empires we were in contact with. We expanded that to the world. We expanded that to the solar system, surrounded by a celestial sphere of stars. We expanded that to the galaxy, and then we expanded that to billions of galaxies in an 'observable universe' 14 billion years old. We can't see any further, but extrapolating from what we can see, we're pretty sure there's much more of it out there beyond the horizon. Infinitely more? No way to tell. It is currently (and arguably) the simplest model. That's all.