What's the difference between " lean against " and " rest against", please?

For instance:
1. The professor is leaning/resting against the blackboard.
2. A shovel was leaning/resting against the wall.

Thank you very much for your reading.

Question

What's the difference between " lean against " and " rest against", please?

For instance: 
1.  The professor is leaning/resting against the blackboard.
2.  A shovel was leaning/resting against the wall.

Thank you very much for your reading.

Answer

1. Resting may imply the teacher was tired. The teacher could be leaning against the blackboard and still be actively teaching.

2. A shovel can lean or rest against a wall.

An object at rest is not moving.
A person resting may have some movement.

Answer

"Lean" suggests a slight angle with the vertical.

"Rest" does not suggest anything about position. You can even be horizontal while you rest. In fact, that's what we do when we sleep.

Answer

They have the same meaning, they are interchangeable.