That's framerate (how often images need to be rendered) at 60hz. Latency is separate from that: you can have a 60hz framerate with 24h latency if you watch a video you recorded yesterday.
In the parent's case, 20ms latency from movement to visible motion is part of the pipeline that:
- reads input
- evaluates solution
- returns solution to your screen
All kinds of things add to this latency: polling frequency of your input device, bus speed of the device, how fast you can update the world, how fast you can render the update, how quickly that updated image can be sent to the screen, how quickly the screen is able to turn this into visible light. etc.
60FPS ~= 16.67ms/frame. So if you don't want to drop frames on a 60Hz monitor, your frame time budget is 16ms. If you want input to appear on the next frame, you've got at most 16ms. If you're targeting a 120Hz monitor then you've got 8ms. Etc.
In the parent's case, 20ms latency from movement to visible motion is part of the pipeline that:
- reads input
- evaluates solution
- returns solution to your screen
All kinds of things add to this latency: polling frequency of your input device, bus speed of the device, how fast you can update the world, how fast you can render the update, how quickly that updated image can be sent to the screen, how quickly the screen is able to turn this into visible light. etc.