Back in the olden days, LinkConnect[_LinkObject] was the way you connected a link, and it was the top-level equivalent of the C MLConnect() function. Then it was decided that LinkOpen was insufficiently sugary, and we needed the more convenient functions LinkLaunch, LinkListen, and, hmm...what to call that third one...yeah, it was called LinkConnect. So, LinkActivate was added as an alias. Subsequently, the MathLink C function MLActivate() was added; MLConnect() remains, but the two functions perform exactly the same function.

As it turns out, both definitions could exist side-by-side, since the new expression of LinkConnect had no valid signature involving LinkObject. The version of LinkConnect which takes a LinkObject does not use LinkOpen; look carefully at the signatures and you'll see that. Instead, it directly calls a C function which calls MLConnect().