Essentially, these are just different standards to allow us to deliver the same wireless internet based service.
LTE is a more recently developed 4G standard which has been widely adopted by service providers and equipment manufacturers around the world. LTE is the same standard that is being used in 4G mobile phones.
The main difference between the Home Gateway (LTE) and the Vividwireless WiMAX devices is that the LTE device uses a different channel bandwidth. LTE devices also require a SIM card which isn’t used in WiMAX devices.