The existence of an S strain and an L strain remains controversial in the scientific community, at least in terms of these being distinct contagions. Viruses evolve continually, so there are likely to be hundreds of strains at any given time, spreading in the population. However, the vast majority of these variants create no meaningful differences in the way the virus transmits, causes symptoms, or how patients are treated in the clinic.
Data from the Fred Hutchinson Center in Washington are tracking the evolution of the virus (https://nextstrain.org/ncov) and show hundreds of different mutations across the world as the pandemic spreads. You can think of these differences as similar to the differences between individual humans - the basic plan hasn't been changed, but there are lots of small differences between individual virus populations.
The important part here is that it doesn't appear there is any evidence that immunity to one form of the virus would not also lead to immunity to all the others currently known. It is more accurate to think of the COVID-19 virus as a single strain, as the differences between evolutionary changes are more meaningful for epidemiological tracking and study of transmission than anything medically meaningful at this time.
Drafted 3 April 2020