What difference does it make whether I schedule a new flight via Commercial / Flight Planning or via Operations / Fleet Management / Flight Planning?
It’s mainly a UI difference. Scheduling page adds some handy extra’s for you like connecting flights/insights in existing flights for that route etc. Also makes assigning one flight number to multiple different aircraft easier. You also have the possibility to create ‘theoretical’ flights without actually having to assign an airplane. The other option - the scheduler in the Fleet Management page - provides you with a visual planner for the selected airplane. All assigned flights are shown here together with the turn-around times and maintenance blocks. Also provides a visual overview of potential problems like overlaps in your schedule or missing slots for a flight (eg a flight block in a red color or a yellow rectangle if turn-arounds overlap/are too tight)
Both options have their use cases; up to you to try it out and see which page suits your scheduling work best.
Both options are also mentioned in the handbook:
Some general lecture about scheduling flights: Scheduling Flights | AirlineSim Handbook