Get to = arrive "I get to work at 8AM" - that's when you arrive "I go to work at 8AM" - usually people use this also to mean that 8 am is when work starts, although technically it does not mean that. To go refers to the motion from one place to another, and thus it does not normally refer to the time when you arrive - however it is often used with that meaning, like in this case. The thought behind it is to talk about the contrast between when you go to work and when you finish work, rather than focusing on travel time. So you go to work at 8 and you leave at 5. 'I go to work at 8' is not a very clear expression, as one could understand it to mean that you are leaving home at that time. But usually if people want to specify at what time they leave home to go to work, they say this: "I leave for work at 7AM."

"Get" gives the sense that you're arriving somewhere, whereas "go" suggests you're leaving.

Additionally, If you tell someone to get to work, you are suggesting that they should finally start doing the long delayed work or fixing a long delayed problem. For example, "He promised to get to work on the state's massive deficit." Casey

"Go" is an irregular verb, whereas "get" is not a verb at all. In terms of your two examples, think of them within the context of a itinerary or journey. I will "go" to work at 0800, but I will "get" to work at 0810.