Usually when you have a guitarist who is also the lead singer, they have to be somewhat still while singing. Bang your head and play the guitar and sing WELL at the same time...you can't. One of the three are going to have to suffer, so it's usually the presence when you are in the middle of a vocal line. Ever seen Megadeth live? Dave Mustaine DOES NOT FUCKING MOVE when he's singing. It's almost like his body is dead but his arms and hands and lips are moving. As soon as there is a break in the vocals, just like Hetfield, they start thrashing.
It's also little nuances that James does to get the audience going. He has a very commanding presence and voice as well. A little "yeah!" here or "errrggghh" there adds to the song. Case in point, listen to the Binge and Purge album and all the little ad libs he makes to the songs. He gives them more life when it's live. For instance, at the end of The Four Horsemen, he holds this really loud "YEEEEAAAAAAHHHHHH!!!!!!" before he goes back into the refrain. That's presence. It's not just moving, it's the whole package. Work the crowd, get into your music, and blow it all out your piehole into the mic.