Engineers have (traditionally) three missions: mobility, counter-mobility and survivability.
Sappers were the guys who helped you move by breaking into the bad guy’s fortifications.
Pioneers built and cleared your roads and bridges.
Forts were built by engineers who seem to have lacked a neat name.
The Pioneer in Commonwealth and Continental European armies is a specific subgroup of engineers with a long tradition. There is no direct equivalent in the US military.
The Canadian Army still maintains the tradition of allowing Pioneers to wear full beards, and I have seen parade photos of British and French Pioneers doing the same. The tradition stems from the Pioneer units’ origins as penal battalions that “specialized” in rather risky operations involving explosives and enemy fortifications. The members of these units were often kept under guard and not allowed shaving implements when not in actual battle. Thus, an “elite” of sorts.