When John baptised, he said that he baptised with water. But one (Jesus) would come and He would baptise with fire and the spirit.
I understand that baptism is and outward act used to demonstrate an internal act.
I see them as two different and distinct Baptisms not occuring at the same time. Christ Baptism the one John spoke of with fire and spirit comes at the instant you accept Him as Lord and Savior. IOW it is a spiritual Baptism of your very soul. The second the public profession and baptism usually coming later. Some churches require membership classes etc for that. That is the Baptism of obedience in accordance with The Great Commission.