Is an air-soft gun the same as a pellet gun?

No. First off, airsoft guns are chambered in a larger calibre, they're around .25" ( 6mm ). Modern BB guns are all .177 caliber. Pellet guns can be .177", .22" or .25", but bb's only come in .177 ( unless it's a real oldie which might be in .22 ) Second, airsofts all only shoot plastic balls or paint capsules. .177 BB's are copper plated steel the and the .22's are lead, and most BB guns will shoot the hourglass shaped lead pellets as well as BB's. Finally, airsoft rounds are propelled by a 'hammer" coming up and slamming into the round which drives it out the end of the barrel, BB's are always (so far as I know) propelled by a burst of air.