Hydraulic mining, at least as used traditionally, is when water was sprayed onto a hillside, washing it all downslope and through sluice boxes.

Suction dredging is co ducted instream, where the material on the bottom is sucked up into a sluice box type of contraption.

Don't know of any hydraulicking anymore, the Federal Courts shut it down in CA in the 1880s, i believe, due to primarily agricultural damage. The state, oddly enough, was unwilling to regulate it so the Feds (over)stepped in.

Suction dredging is being hotly contested in at least WA, OR, and CA.