To add an other aspect to the explanation, since this is about education any ways

Most pow algorithms use a hash function, that is we have an deterministic hash function H such that the result of the computation is H(x), where x is a defined part of the block header concatenated with a nonce (that itself has a pool nonce and a client nonce part.

So we evaluate a defined hash function and get exactly one result out of it.

For Equihash algorithms this is different. The name Equihash may be confusing here, because Equihash is in fact no hash function!

Here it works differently: We compute a dataset H(x_i), where x_i is a concatenation of the block header fraction plus nonce plus i (as 32 bit representation), where i ranges from 0 to 2^(m+1) with m=n / (k+1) … thus 2^22 elements for Aion. H here is indeed a hash function, concretely blake2b algorithm.

But this is only first part of Equihash. Now with the many hash results a 2nd phase starts where we compute opportunities to the problem “take 2^k elements from the previously computed set such that they xor to 0” (plus some other side conditions)

The result/the solution is then what makes a share. So we do not have a real hash function, but compute solutions to a mathematical problem, thus the term Solutions/second or sol/s makes sense.

Note that on average 2 solutions in each Equihash iteration are computed, but for a single iteration the number can be anything - 0,1,2 and more. Max I have seen so far in a single iteration was 7, but in theory there is no upper cap.

This is also the reason why Equihash solution rates fluctuate so much - the number of iterations per second is rather constant, but the actual computed sol/s is a bit luck dependent.

The other terms that one often reads when it comes to hashrate - giga (G, 10^9), mega (G, 10^6) and kilo (K, 10^3) are only factors that make reading more easy. Finding Equihash solutions take rather long, so it makes sense for one GPU to speak of sol/s, while e.g. for Ethereum each second more then 30’000’000 hashes can be computed in one second, so here 30 Mh / s (Mega hashes / second) is easier to read.