We used Port of Cadiz Bay (Puerto de Cadiz) twice - first for entering from El Puerto de Santa Maria, second for leaving back to, yes you re right, back to the El Puerto Santa Maria again.
At Reina Victoria pier in Cadiz-City Basin, there is a metropolitan maritime station from Cádiz, that attends to the passengers between Cádiz, El Puerto de Santa María and Rota, with modern catamarans. It has it access from Sevilla square and it is five minutes walking from the center of the city.
Inside terminal building
Passengers leaving Port of Cadiz Bay terminal
Puerto de Cadiz