I suspect your confusion might be that Fleetwood Mac has historically performed "I'm So Afraid" in two different keys. Depending which recording you are playing along with, your TAB might be in the wrong key. Part of becoming a good bassist is being comfortable playing songs in any key. Lots of bands perform their songs live in a lower key than the recording, to make it easier on the singer's voice.
Your TAB is of the original album version in the key of G Minor, 2 flats (Bb, Eb). But many of FM's live performances of this song are in the key of F Minor, 4 flats (Bb, Eb, Ab, Db).
If you're playing along with a G Minor recording (like the original album version) then the notes of the bass line are G, D, Eb, C. But if you're playing along with an F Minor version (like the live version on The Dance) then the notes of the bass line are F, C, Db, Bb.
It sounds to me like this song was recorded on a 4-string in standard EADG tuning. The reason John McVie's bass is "deep sounding" is because he is an experienced, tasteful, and skilled bassist. It's a "simple" bass line performed by a master player! He'd been in FM almost 10 years when he recorded this song. If you've been playing less than 10 years then there is no shame if you don't sound exactly like McVie.
The best way to learn this stuff is to find a good teacher. But not all bass teachers are equally good at teaching "ear training"! I took bass lessons for years before I finally got halfway-decent at ear training. The "breakthrough" moment for me, was finding a music-theory teacher at the local college, who was a pianist not a bassist, but who was excellent at teaching ear training. Ask around your circle of musician friends, if anyone knows a good ear-training teacher, who can teach you the skill set to figure out what key your favorite songs are in, and which notes to play on the bass. I would encourage you to use your ears (not TAB) for learning easy songs like "I'm So Afraid."