They have a vision that involves specialized mining hardware running people with enough data storage and upgrade capabilities to maintain a full node that would result from an increased block size. They see users as running the SPV wallet while miners maintain the network as well as full node.
The real/ original Bitcoin (call it Bitcoin core if you like) vision is to always keep it possible for anybody willing to give the time to be able to run a full node with hardware investment not being an entry barrier.
Seriously? Have you ever read all the stuff Satoshi actually said? Go read the whitepaper and all his emails. What you'll find is that "bitcoin" as it is today and the direction core is taking it, is not what he envisioned. He envisioned exactly what bitcoin cash is. One can argue that what core is doing is the right path and that Satoshi designed a flawed product that they need to "fix". But he said miners would run full nodes and users SPV wallets. He said when they needed bigger blocks they'd just do a fork to increase the size. So please don't imply what core has done with bitcoin is the original Satoshi design/vision.
For the record, I think both coins are fundamentally flawed and will never be able to achieve what people really want, which, IMO, is to have a completely decentralized currency with which to buy a cup of coffee without having to pay some ridiculous fee.
I have read the emails and whitepaper. Lets keep that settled.
The vision i talked about is the difference between the visions of BCash and BTC. Not Satoshi's vision per se. Maybe you should argue on that without bringing Satoshi into it.
Of course he wanted miners to run full nodes. He assumed that anybody with a CPU and willing enough would be able to mine. 1 CPU=1 Vote right?? That would have been correct on his part if it was possible for everyone to be a miner and run a full node.
In reality, being a miner now needs specialized ASICs with thousands in investment(which he did not envision). When he said that users would use SPV wallets, he meant that for a scale where everyone and even the most non-tech people would be the users. Of course, they wouldn't run nodes.
The nodes would still need to be run by a vigilant community of technologists and hobbyists. Mining was taken away by ASICs and now Full nodes too go away in Bcash vision with a higher block size. (without the underlying improvements)