Both AutoCAD and Revit contain the function "nudge" - for nudging, pushing of selected objects in a certain distance using the respective arrow-key on your keyboard.
It is an inaccurate operation not suitable for moving the drawing geometry, but it can be useful e.g. for fine-tuning placement of texts, annotations, legends, etc.
In AutoCAD you can invoke nudging of grip-selected objects by pressing the combination Ctrl+arrow (up, down, left, right), in Revit just press the arrow key.
The nudge step size depends on the current zoom level - so it is measured in "pixels" rather than in drawing units. In AutoCAD Snap mode (F9), the nudge step size is equal to the current snap size (see SNAPMODE and SNAPUNIT).