most "professional" streamers will have a separate encoding/streaming PC w/ some sort of capture device (commonly one of those Elgato capture cards). They'll then hook in their main PC or console into the capture card.

Main reasons for this are to eliminate the overhead of reencoding video in OBS w/ multiple layers of images/videos/donationAlerts/etc which can have a negative impact on the game (or other software) they're trying to stream.