An earlier Hint showed that to and toward are
generally used with verbs showing movement
and that to often shows the result of the movement
while toward shows the direction of the movement.
In addition, the earlier Hint noted that to can be used
for toward, but toward cannot be used for to.

The prepositions in and into and on and onto have
somewhat similar "behavior."

Into and onto are used with verbs showing movement.
They show both the direction and the result of
the movement.

In and on may be used both with verbs that show
movement and with verbs that do not show movement.
With verbs showing movement, in and on may be
used instead of into and onto (though into and onto
are clearer). In this case, they show both direction
and result. With verbs that do not show movement,
in and on show location: in = inside or within
and on = topside or touching the surface of.

Examples

Fouad dived into / in the lake.

Fouad says that the water that's in (not into)
the lake is cold.

Chang-Ho threw his keys onto / on the table.

Chang-Ho left his keys on (not onto) the table.

Nadia put the cake into / in the oven.

Nadia will leave the cake in (not into) the oven
until it has finished baking.

The cat jumped onto / on the sofa.

The cat lay on (not onto) the sofa all afternoon.