Howdy Grapeshot,
Pioneers were part of an Infantry Regiment. One in each company, for 10 in a Regiment.
Sappers were troops of the Corps of Engineers. During the War of 1812 they were called "Sappers, Miners and Bombadiers" Sappers dug trenched to attach fortified places. Miners dug under walls and Bombadiers placed the explosives to blow up the wall. By the ACW the Engineer troops were called "Sappers, Miners and Ponteneres [sp?] for placing pontoon bridges.
In the Royal Engineers the are simply called Sappers. Brit. Infantry Regiments had Pioneers too. They were the only troops allowed to have full beards up to the 1850's, I think.