Ocean Trench 1

Seafloor spreading is the mechanism by which new seafloor lithosphere is constantly being created at mid-ocean ridges. This theory, introduced by Harry Hess, was proven as patterns of magnetic field polarity preserved in seafloor basalt and by age dating of the rocks.\
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Continental drift theory is related to the movement of contintents which was once a super large continent named as pangea. While in seafloor spreading magma from the upper mantle arise along weaker zone or in between two plates spread and form a new oceanic crust. Not a difference: just two aspects of the same thing.
Basically, sea floor spreading (which isn't a theory, but a fact - you can see it happening in real time on land in Iceland) is how continents 'drift'. Once the continents were mapped, people noticed how neatly you can tuck South America into Africa (for instance) and there was speculation that the continents used to be 'together' and now of course they aren't. But exactly how that might happen wasn't at all apparent, and there were a number of ideas (some of them genuinely silly) about it.
Once we began being able to measure the age of the ocean floor however, the theory of plate tectonics was developed and tested, and now we know (not speculate) that mantle rises and cools to form new ocean crust along the mid-ocean ridges, and older oceanic crust is subducted (carried downward back into the mantle) and recycled/destroyed at the trenches. The continents are carried along as the new crust moves away from the spreading centers and toward the trenches.
Compare continental drift and seafloor spreading
In 1965, a Canadian geophysicist, J. Tuzo Wilson, combined the continental drift and seafloor spreading hypotheses to propose the theory of plate tectonics. ... The term “continental drift” was no longer fully accurate, because the plates are made up of continental and oceanic crust, which both “drift” over Earth's face.