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Full Idea
According to Newton mass is conserved, while in Einstein's theory mass is not conserved but can be converted into and from energy.
Gist of Idea
In Newton mass is conserved, but in Einstein it can convert into energy
Source
Alexander Bird (Philosophy of Science [1998])
Book Ref
Bird,Alexander: 'Philosophy of Science' [UCL Press 2000], p.278
A Reaction
Perhaps this is the most fundamental difference between the theories. It certainly suggests that 'mass' was a conventional concept rather than a natural one. Maybe the relative notion of 'weight' is more natural than 'mass'.