As an adverb, what is the difference between forward and forwards?
The OED says this
The present distinction in usage between forward and forwards is that the latter expresses a definite direction viewed in contrast with other directions. In some contexts either form may be used without perceptible difference of meaning; the following are examples in which only one of them can now be used: ‘The ratchet-wheel can move only forwards’; ‘the right side of the paper has the maker's name reading forwards’; ‘if you move at all it must be forwards’; ‘my companion has gone forward’; ‘to bring a matter forward’; ‘from this time forward’. The usage of earlier periods, and of modern dialects, varies greatly from that of mod. standard English. In U.S. forward is now generally used, to the exclusion of forwards, which was stigmatized by Webster (1832) as ‘a corruption’.