Do speaker cables really make a difference ?

Yes. And so do power cords, interconnects, digital cables, ethernet cables and even outlets. 

They definitely do and probably more than any other cable, then power cables, interconnects and digital cables the least. At least that’s my opinion. If you can’t hear the difference in your system then you should probably start with upgrading your speakers first.

They certainly can do so.  I recently replaced long runs (6m) of thick (6sqmm) van Damme cables with Neotech NES 3002 cables  Big price difference.  The Neotech are made of OCC copper and have multiple thin cables in much better insulation.  The result was that good recordings sound much better: more detail and better sound stage.  Bright recordings now sound a bit too bright but can be tamed inexpensively with a Schiit Loki.

Here's a link: https://wp.neotechcable.com/up-occ-copper-cable/

As far as I understand (not very far really) one factor explaining the difference is the  difference in skin effect between one thick cable and lots of little ones which together have the same volume as the thick one.

Positively YES! Just let your ears be the judge.

Yep ….

Need proof? The next time you attend a hifi show, take a moment to look behind the systems in your favorite manufacturers’ rooms. You’ll notice that the cables they choose to use when they’re trying to make a good impression are not the standard cheap or middlin’ cables. They only use very top end premium OEM brands - and only the very top OEM brand models - to showcase their components in the best light possible.