Earlier quoted context omitted.
The traditional meaning of an $x billion company is by revenues. Using it to mean valuation is quite new, and limited to startup/Silicon Valley people.
I'm pretty sure Wall St. people also talk in terms of valuation.
In general, Wall St tends to use this nomenclature (i.e., $X billion dollar company) when referencing revenues. For instance, Procter & Gamble is referred to as an "$80 billion dollar company" - which speaks to revenue, not market cap.
This gets murky with private firms, since revenue isn't typically shared, and even more so with startups where so much of the value is based on future, projected earnings.
In general, though, I'd say the nomenclature more commonly refers to revenues and not 'valuation'.