I see these terms as being subsets of one another.

The 'universe' is everything that came out of 'our' Big Bang, and includes regions of space that are currently so remote from us that in the 13.7 billion years since the Big Bang, light has not had time to reach us from these distant regions. The portion of this space that we can now see is called the Visible Universe. It has a radius of 13.7 billion light years. This limit to the Visible Universe is expanding as the universe expands, and will grow larger in the future. However, because the expansion of the universe is accelerating, our visible universe in the unimaginably distant future will never equal the actual scale of the universe.

The knowable universe includes the portion that we are now able to see, and also the portion which is still beyond our current information horizon. Big Bang cosmology says that there does exist a larger portion of the universe 'out there' beyond the limits to our visible universe, but that the universe is not yet old enough for the light signals to reach us from there yet. As the universe gets older, more of this currently unobservable, but knowable, universe will come into view. There are, however, NO observations we can now make that prove that this other part of our universe exists at all.

Again, because our universe is accelerating in its expansion, the knowable universe will never include the entire space and collections of matter which actually emerged from the Big Bang. In fact, in the remote future, the volume of the knowable universe will shrink to a mathematical point in relation to the volume of space then avilable to the universe.

As for the term 'universe', some feel it should include other 'universes' and other spacetimes. I disagree. A new term is required to describe these other places because they have, at least mathematically and physically, no connection with our universe. This is why 'multiverse' is coming into increasing usage in some sectors of astronomy. Although predicted theoretically, they are not a part of what came out of our Big Bang, and they are forever unknowable. Curiously, mathematics and 'logic' allow us to speculate what these other universes might look like so they are unknowable from the observational sense, but not beyond logical speculation.

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