What is the difference between osmolarity and molarity?

Molarity is the concentration of solute molecules in mole/liter of solution.

Osmolarity is the concentration of solute particles in mole/liter of solution.

When does molarity = osmolarity?

Molarity = osmolarity when the solute does not dissociate in the solution. Examples of such solutes are glucose, urea, glycerol ...

What is osmosis?

Osmosis is the net diffusion of water from one region to another.