a sapper is someone who went through the sapper course, which is a combat engineer version of the ranger course (mentally harder, not sure about physically).
the army equivalant of USMC infantry is...wait for it....army infantry. yes marines basic is 13 weeks and the army's is 9, but the first 4 weeks of USMC basic are wasted on D&C and learning the USMC history, where as every day of hte army's 9 weeks are spent on combat training. infantry osut for the army is 14 weeks btw.
marines dont really have just set "infantry" though. each position in a squad is a different MOS that focuses primarily on their weapon systems (240 vs m16, etc). army infantrymen use and train with EVERY weapon system at their units disposal.
what you learn in TRADOC though doesnt really mean much, since you'll relearn everything at your unit, and the army definately has a larger budget. that means more rounds to use at the range, more time in the field, and better training.
if you dont believe me, find the casualty rates for the 2 branches: a marine is 1.8X more likely to die than a soldier. and a LARGE percentage of soldiers who didnt make it back were jobs like 88M and other support MOSs that the marines dont have.
anyway, a sapper is the above ground equivilant of a sailor who went through BUDs.
Force recon is the equivilant of a LRS-D section in the army...though i might argue that since LRS sends all of its members to ranger school, airborne school, air assault school, sniper school, and pathfinder school (if time permits) then honestly a member of LRS probably has more training than a member of force recon. but again, tradoc is only a small part of the equation: experience is most everything and both of them get plenty.
MARSOC is the USMC equivilant of the army's rangers
they dont ahve any equivilant of special forces, SFOD-D, etc.