i wont buy an s1 so if someone told me it was an s4 i would probably throw it in the trash lol.
heres a quick simple break down. f1 (first gen) so a hybrid of 2 different strains, f2 (second gen) or a male and female from the f1 seeds crossed together, f3 (third gen) so 2 of the f2 plants crossed together.
bx1 (back cross 1) you take an offspring from the f1 seeds and cross it back to one of the parents, bx2 (second backcross) you take one of the bx1 plants and cross it back to the original parent. this is also known as cubing and is to try and lock down some of the original parents traits.
s1 (selfed 1st gen) as said above a plant is forced to produce ale flowers and pollinated to itself or a clone of itself. this should produce pretty similar offspring to the parent plant. however it comes at a cost, s1 lose vigour and yield so you end up with a slow vegger which doesnt quite produce the same way its mother did. im not totally sure how you would make an s2 but im thinking picking your best from the s1 and selfing that plant would give you an s2
hope that helps.
P.S at least that is how i have always understood it. by all means if i am wrng please do correct me. there is enough bad info floating around out there already lol