Is there a difference of spacing between cogs on a 7 speed cassette vs a 8 speed cassette?
Yes, there is. Shimano/SRAM &amp; compatible seven speed is 5mm cog-to-cog, and eight is 4.8mm. Generally what you're trying to do here can't be made to work very well. There are some tricks that without any additional parts can increase the movement of the derailer, but not decrease it. Also if you have a true 7-speed-only chain (not common anymore but they exist, KMC Z50 is one example) it won't work well on 8.

A shop not having anything to offer to make the conversion work is pretty unfathomable. The "correct" spacer is a 4.5mm one, but the only thing that makes it correct is that's the number that locates the cassette exactly where an actual Shimano 7-speed hub would, so you could theoretically swap wheels without adjusting the derailer. Any other stack of correct internal diameter spacers in the 4-5mm or so range will still work, so if this shop was too new-stuff-oriented to have a 7->8 spacer, they should just sell you a 2.5mm bottom bracket spacer (ubiquitous modern shop item) plus a 1.8mm 10->11 hub spacer (ubiquitous modern shop item). That will work perfectly.