Adventure games are where you go around and solve puzzles and talk to people. There is usually not combat, especially reflex-oriented combat. Adventure games are hardly ever made these days.
Examples: The Secret of Monkey Island, Syberia, Day of the Tentacle, Grim Fandango, The Longest Journey, Myst, Still Life
Platform games are where you control something that can usually jump high and jump around on platforms to accomplish some goal.
Examples: Super Mario Bros., Sonic the Hedgehog, Super Mario Sunshine, Yo! Noid, Ristar, Jak & Daxter
"That Mormon almost destroyed my left hand." ~TEM