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Inflation in cosmology refers to a phase of the early universe where the universe expanded extremely fast. And the universe expanding quite literally means the space getting bigger.
As you noticed, cosmic inflation does not refer to just any expansion of the universe. The universe is still expanding, and the expansion rate even increases, but that is not what the term cosmic inflation refers to; it is only the extremely fast expansion that must have occurred in the very early universe that is referred to with this word.
As driver for this ultra-fast expansion, cosmologists hypothesise a so-called inflaton field which drove the expansion, and which essentially disappeared at the end of inflation.

Inflation in cosmology refers to a phase of the early universe where the universe expanded extremely fast. And the universe expanding quite literally means the space getting bigger.
As you noticed, cosmic inflation does not refer to just any expansion of the universe. The universe is still expanding, and the expansion rate even increases, but that is not what the term cosmic inflation refers to; it is only the extremely fast expansion which according to at least one theory in this direction, must have occurred in the very early universe that is referred to with this word.
As driver for this ultra-fast expansion, cosmologists hypothesise a so-called inflaton field which drove the expansion, and which essentially disappeared at the end of inflation.