We went round and round about this particular bit of nomenclature when we first set up the trail reports section of the website. I think the Bear Basin Trail and Connector is possibly the most arguable set of names on the entire district. Anyway, as I recall, we ended up deferring to the Sierra Club guidebook since it's the longest-standing trail guide available. Here it is, from the 6th edition, page 25:
"From (Pine Valley) camp itself, the Bear Basin Trail leads steeply uphill. The trail is marked by a sign. This trail climbs to a saddle where there is a trail junction. The Bear Basin connector to the left leads uphill to intersect the Pine Ridge Trail, providing a shortcut for hikers using the Pine Ridge Trail to the west; the main trail drops steeply down to Bear Basin. The Bear Basin Trail continues through the basin, climbing to join the Pine Ridge Trail at a point 1.6 miles west of the lower Bear Basin connector."
