The various universes within the multiverse are called "parallel universes", "other universes", or "alternative universes". It is possible to classify a multiverse based on what types of universes it contains and how they relate to each other as shown on the Altverse page.
There can even be multiverses with different properties within the Megaverse.
There are different ideas of what a multiverse is, but the basic idea is alternate versions of our own reality and put on an infinite or finite level. However, the structure of the multiverse, the nature of each universe within it, and the relationships among these universes differ from one multiverse hypothesis to another.
The term was coined by physicist Willliam James.[Wikipedia 1]
The dimensionality of a multiverse depends on the specific interpretation of the multiverse taken.
The simplest conception of a multiverse is five dimensional, with several four dimensional universe-lines arranged in a stack in the fifth dimension. (An alternative, even simpler thought is that they are actually four-dimensional like our universe; universes within would just have three-dimensional spacial boundaries like bubbles.)
Imagining the Tenth Dimension conceives them as being six dimensional, with the fifth and sixth dimensions representing different directions that a timeline can be diverted to create alternate universes.
The most extreme conception of the multiverse has them be infinite dimensional, with the coordinates of a point in the multiverse representing the complete state of the universe located at that position (such a multiverse can also be called a phaseverse).
Multiverse Vs. Omniverse
Really, it's all about terminology. However you define a/the Multiverse can be a way to describe the Omniverse as well. One could say the very prefix 'Omni' (All) could put the Omniverse above Multiversal level, say the Multiverse contains 'Multiple' realities but not exactly 'all'.
Think about it this way: There are several Multiverses in fiction, such as Marvel, Doctor Who, DC, Saint Seiya, Lego, Futurama, Kingdom Hearts, Half-Life, Dark Tower, whatever. They are all brought together within the Omniverse, containing all fiction and non-fiction. In other words, they're bound by copyright and stick to their own continuity and only occasionally interact, meaning each Multiverse is their own 'everything' or 'reality'.
For Megaverse, the concept itself is just a way to help keep a separation between the Omniverse and Multiverse, for whatever concepts may be outside the very concept of a Multiverse or perhaps just a standalone Universe.
Relax, this isn't any Hyperrealist statement or anything, just explaining fiction and it's affect on the Multiverse/Omniverse concept, we know the difference between fiction and non-fiction.