There are some airlines where a multi-segment flight with the same flight number does stay on the same aircraft through all of the segments, but that is not true for all airlines. Where it is not true, there is the usual risk of missing the connection and the like.

WN 2325 is flight where the same aircraft goes from OAK->MSP->MDW->PHL. A passenger can book it on Southwest's web site, which shows it as a two stop flight with no plane change.

However, UA 497 uses different aircraft from the EWR->SFO (777-200) and SFO->SAN (737-900) segments.