The difference lies in the type of state they are in. When M is mentioned it means it refers to a solution while mol refers to pure substance.
Thus,
0.5 mole of Na2CO3 eans that 3.01 × 10^23 molecule and also about the molar mass of it i.e. 53g
0.5 molar Na2CO3 means that 3.01 ×10^23 molecules or half mol Na2CO3 dissolved in 1L solution