Megabits per second is an internet speed rating.
Gigabits per second is a LAN speed rating.
Cooper ethernet cableing currently tops out at 1Gbps with RJ-45 Category 6 (or 5 Enhanced) cabling for commonly available ethernet based components.
There *IS* a spec for Category 6 Enhanced for up to 10 Gbps, but NO standardized adapters or infrastructure (switches, hubs, routers) are commonly (cheaply) available.
Internet connection speeds (even for the legendary "Fiber" internet packages, which are still ethernet to your house, and Fiber-Optic from a common switch to the ISP) are still measured in Megabits per second.
DSL: 1-5 Mbps down, up to 1Mbps up, dedicated speed per line.
Cable Internet: 5-30 Mbps down, up to 3Mbps up, shared with your neighbors, as if you were on a hub.
T1: 1.5 Mbps, dedicated bi-directional.
T3: 45 Mbps, dedicated bi-directional.
OC class lines: dedicated Fiber Optic internet, Mb or Gb rating determines speed, bi-directional.