Cosmic inflation says that in the first 10 ^ (-32) of a second after the Big Bang the universe expanded by a factor of 10 ^ 78 and then quit expanding so fast:
Dark energy says that the universe is now slowly increasing the rate at which it’s expanding:
Inflation and what’s going on right now with the “dark energy” are qualitatively similar, and might (or might not-- we don’t understand dark energy nearly well enough to say) stem from qualitatively similar causes. The major (and possibly only-- see above disclaimer about our ignorance) difference between them is quantitative: Under inflation, the Universe had a doubling time of a tiny, tiny fraction of a second, while currently, the Universe has a doubling time of billions of years.