Assuming he is on AT&T, basically "4G" on AT&T is faster 3G, 3.5G if you will, and LTE is "true 4G" as some like to consider it. AT&T as well as other providers broadcast their 3G Data using HSPA. AT&T also broadcasts HSPA+/HSDPA which is faster than standard 3G HSPA service, and thus they market their HSPA+/HSDPA network as "4G". LTE however is what many consider to be "true 4G" as it is extremely fast and reaches speeds that many expect from a 4G service. You may read that HSPA+/HSDPA has theoretical download speeds of something like 14.4 Mbps or higher. This is not something you will not see here in the U.S. I had an iPhone 4S and now a 5 both on AT&T and when on "4G" I never saw anything above 6 Mbps and most of the time it was around 3 Mbps. With LTE I have seen as high as 53 Mbps which is faster than most household internet services.
On his 5 he will notice that when he makes a phone call the phone will switch from LTE to 4G. This is because Apple combined the LTE data and the voice chip into one single chip. While the "4G" data chip is still separate. So when using the LTE/Voice chip to make a phone call, the phone maintains a data connection using the "4G" data chip.
Odds are if he is switching back and forth between LTE and 4G then he is probably in an area where not all the AT&T towers have been equipped to broadcast LTE, while some are equipped to do so. So when he picks up reception from the towers that do have LTE then he picks it up and uses LTE, and vice versa when he picks up reception from a 4G tower, he uses 4G and the phone indicates accordingly.
Hope that clears things up.