Actually, they're the same thing: both are computed as (number of shares outstanding) * (price per share).

The difference is that market cap is used for companies that have IPO'd (and therefore have a broad market for their shares with continuous price adjustments) versus companies that have raised money through private markets (and therefore have infrequent price adjustments).

One can reasonably argue that valuations are less precise than market caps as a result, but both are dictated by sophisticated investors and should be more or less correct on average.

(In fact, valuations are less precise, but this has a lot more to do with the amount of uncertainty inherent in any early-stage company than it does with the availability of shares on a public market; Wall St. has its ups and downs just like Silicon Valley.)