Difference between Catch on to something and Catch up to something

catch on to something—figure smth. out; understand smth.:

• His sagacious mind immediately recognized and caught on to the only plan of salvation in sight.

catch up to something—(also: catch up with something )

1. overtake a bus, etc. by walking fast:

• Jane caught up to the bus that had almost left her behind.

2. keep pace with smth.:

• Quite frankly, at our current pace, we will never catch up to fixing our infrastructure deficit.