You can burn coal and wood in a M/fuel burner, you can’t burn coal in a wood burner, coal needs air from underneath to burn. Therefore M/Fuel burners have a grid and ashpan whereas wood just burns off the floor of the stove. Coal gives off more ash than wood and needs emptying more often.
Coal does have some benefits; if you want to keep the fire on overnight or if you must go out for a few hours the fire will stay on with coal wood will burn out in a couple of hours. Good quality coal burns 9 hours or longer if the airflow is regulated. Whereas logs will burn out after about an hour or two.
I recommend having a good base of coal then putting logs on as needed.
– William Evans