Performer of If You're Going to San Francisco

The song is by The Mamas and The Papas and that version is the live version. They have an album with live tracks.

The original version, and hit, was performed by Scott McKenzie, not the Mamas and the Papas. The Mamas and the Papas did cover it, which isn't too surprising, since John Phillips actually wrote it, and played on the record. No Mamss, or the other Papa, though, and the original voice was 100% McKenzie.

I don't know why Phillips gave it to Scott McKenzie. I suppose the subject was a bit "off" for the Mamas and the Papas, since they identified as transplants to SoCal, not Northern California. Anyway, LA is frequently referred to in their songs ("I'd be safe and warm / If I was in LA," "... in LA, you know where that's at"). The approximate thematic equivalent in their canon was "Twelve Thirty (Young Girls Are Coming to the Canyon)." Perhaps unsurprisingly, Scott McKenzie flipped it around and himself did a cover version of "Twelve Thirty."

I can't tell what the version over the credits is. It's not the original record, and does pretty obviously seem to be live. It could be the Mamas and the Papas; if not, most likely Scott McKenzie. There must be hundreds of live recordings of him doing it, since his career for the last forty years primarily consisted of playing that song (until he died, about a year ago). The arrangement is almost exactly dead-on with the original. The presence of a backing vocal, which comes in part way through, suggests the Mamas and the Papas, though Scott McKenzie performed with backing vocalists too, particularly in more recent years.