6, 7 and 8 speed chains are the same width at about 7.1 - 7.2mm, whereas 9 speed chains are usually up to 6.8mm.
The 9 speed set up is designed with correspondingly narrower gaps between the cassette sprockets and so using a 7 or 8 speed chain, although only ~0.3mm wider will not be very easy to index properly.
Not sure what the effects would be in terms of wear, only in terms of shifting performance.