While possible, the notion that asymptomatic[†] cases are due to a separate less-pathogenic strain is both indeed a possibility researchers are thinking about, and yet also not (a priori) the only or perhaps most probable explanation for the wide variance in clinical outcomes we see. Other important, perhaps dominant, factors include heterogeneity in people's immune responses to virus--common in other conditions--and (possibly) a dose-dependence (e.g. if you are exposed to a high viral load e.g. by intense or prolonged exposure, some reports (but far too few for definiteness yet) are that clinical outcomes may be poorer). Though there are different COVID strains in circulation (see the amazing data tracking of https://nextstrain.org/ncov), with regards to the proposed hypothesis: there is no evidence that these strains show any difference in virulence (see e.g. the perspective of Francois Balloux at UCL: https://twitter.com/BallouxFrancois/status/12395362423558225...). Many groups are attempting to scale up environmental genomic testing for COVID (see again the nextstrain site).

[†] Note that currently, researchers are rather vigorously debating the true proportion of asymptomatic cases (or distinguishing them from pre-symptomatic cases)--we need more widespread e.g. antibody-based testing to answer this more confidently than we can by indirectly fitting coarse time-series to simplified models.