Shoring is to keep something in place from moving (structural members, dirt ....). It is mostly done at temp work while getting required construction work is done such as replacing supports or placing new structure to keep affected construction from displacing.
On the other hand piling is to provide permanent support. Piling can be used for vertical and horizontal support. If you want to support such as soil from displacing horizontally, you use sheet piles (which also has vertical support capacity) vertical piling can be timber, precast, auger cast, pipe, H pile ...
