s1 is indeed similar to f2 in that sense.
however, with an f2 you usually don't know exactly how similar those 2 parents were genetically, while with s1 you know the parent was exactly the same.
so for an f2, you might be dealing with more than just 2 variants(alleles) of a gene, since theoretically, there are different 4 options that could have ended up in your seed(only if those were present in your genepool, i.e. the parents of the f1, to begin with ofcourse, but theoretically, if there were 4 or more variant present in the genepool, both f1 plants could be heterozygous with 2 different variants as the other).
with s1 you know for sure there are only 2 options, since the parent-plant only has 2 of each gene you know for sure no matter how many were present in the genepool, only 2 you can find in your s1-seed(from 1 plant, not mixed s1-seed from different plants).
and since there are 2 versions, you also know for sure that each plant grown from s1-seed will be about 50% homozygous(statistically, so if you have advanced genetic tools at your disposal you can go to a homozygous line quicker by choosing those that have a higher%, but if you don't have those tools you just have to go by the statistic chance, which is 50% each generation, so s1=50%homozygous, s2=75%, etc).
with f2, that statistic % is smaller. not feeling like doing the math right now since I'm here in my break from studying for a math-exam, but you can see the principle without seeing the exact numbers.
but if you know for sure that a recessive gene is present in heterozygous form in both your f1-plants, there's no difference. like a cross between an autoflower and photo, all those f1's will have one autoflower-gene, so wether you do f2 or s1 with the f1, always 25% will be full autoflower. because you know there are only 2 variants in your genepool, and you know all the f1 are heterozygous for it.
but for all those genes you aren't explicitly keeing track of, or you don't even know for sure how they inherit, or they just have a small effect, selfing helps you to stabilize quicker.
