These are both excellent informal phrases for certain situations. The Situation: You see a person or people who is (are) doing something/completing a task/progressing in work, etc. and you want to tell him/her/them to continue. Maybe the person/group is having difficulty, maybe not; in either case you can use these phrases. @Chris is correct because both of them mean the same thing: "Continue!". Now, for me (a male Amer. English native speaker about 24 years old), the difference that I see between them is only how or when I would pick one to use. I would use "Keep it up" in almost any situation to speak to the person. Any time that I see that situation from above I could say "Keep it up". My opinion is that it is direct and personal to the person or group, and I am speaking to him/her about their own motivation and mentality. Example: I am running 5 kilometers on the beach and I see someone ahead of me running with difficulty. If I pass him I can say "Keep it up!" (Continue running! Don't stop!) I would more likely say "Keep going" (I would not use the "it" but you can) if I met people who had a job or plan or another "thing" that they were doing, so for me it is less personal about their motivation and more about their action. Examples: In the street I meet two people who set themselves a challenge to walk 100 kilometers to ask for money to cure cancer. I would tell them: "Keep going" (Continue doing your challenge which is the action, nothing about the people.) In my apartments, the fire alarm begins to ring at 10:00 p.m. I go out my door and meet my neighbour in the hall, but I remember that I should turn off the oven in my kitchen. While the alarm is ringing, I go inside for 15 seconds but I tell my neighbor "Keep going (Continue your action to exit). I will finish in a second." I hope that this helps you to understand. I had to think about how I use these differently, and that is just me. Good question.

They are basically the same thing. You might use one over the other depending on the context, but you would interpret them the same way.

Thank you Cameron!! :D

"Keep it up" could also be said as a way of encouragement. "Keep it up. You can do it". While "keep it going" could be more of a phrase to encourage a worker to meet their work goals. "Keep it going. Keep it moving. We need to meet production goals". Like Chris said, it depends on the context. Let me know if this helps and feel free to ask me for help anytime.