Sol/s measures the rate at which Equihash solutions are found. Each one of those solutions is tested against the current target (after adding to the block header and hashing), in the same way that in Bitcoin each nonce variation is tested against the target. That is what we mean by Sol/s === H/s - they are measuring the same thing, and it is the same metric that everyone already uses for other PoW algorithms. Put another way, measuring Sol/s in Zcash is exactly the same as measuring TH/s in Bitcoin (ignoring the "T" scaling factor, which is merely a product of the relative speeds of the PoWs and the relative numbers of miners).
The problem with using H/s is not that the base metric is wrong, but that there are several metrics that could be picked, only one of which is the same as what users expect. In the screenshot above, NiceHash have incorrectly picked the metric "Equihash runs/s" as equivalent to H/s, leading to user confusion (because users will look at that and compare it internally to Bitcoin's TH/s). By using "Solutions/s", it is completely unambiguous to both miner developers and pool developers which metric it means, and it ensures that users are getting the "right" metric.