Quantize and humanize
Quantize moves notes onto the grid. Humanize scatters timing or velocity by a percentage. Warp markers do the timing job for audio.
Quantize moves notes onto the grid. Set the grid first: 1/8 for a simple part, 1/16 for something busier. Select the notes and press Quantize. With nothing selected, every note in the region moves. The control is in the MIDI editor. If the result is stiff, lower the strength, or follow it with humanize.
Humanize scatters the selected notes. Strength is a percentage. Position moves the start times, duration moves the lengths, and both does the two. A small percentage sounds played. A large one sounds accidental. After a loose take, quantize first, then add a little humanize.
Swing also leaves a straight grid, but the shift is regular: every other subdivision moves by the same amount, and the notes in the region stay where you drew them.
Audio has no Quantize button. Warp markers drag points in the waveform onto the grid one at a time.