I agree with DoctorArcanus - it is not only difficult to tell, but similarities and even overlaps of iconography may even be mis-interpreted as connected when perhaps each derives independently from the common substrata of symbolic images and thought.
Where the difference lies, and importantly so, is that Alchemy has, in some ways, a definite 'common' language it seeks to present in terms of transformation (or transmutation). I'm frankly unconvinced that tarot's imagery seeks to represent the same. At most, it would be a journey towards the spiritual realms, of spiritual awakening, and of gnosis. Though these may indeed have overlaps (in both psychological and spiritual ways), there is a distinct difference of approach and presentation.
Even the cathedral stone carvings - despite Fulcanelli's wonderful writings and suggestions for the same - strike me as distinctly un-alchemical in essential traits. This does not mean, of course, that images arising from the same European soil will not weave and use similar forms, or that the underpinning thoughts will not have their influence on all that arises.
...not sure whether I've actually written this in a clear a manner as I could have!