Do you mean "console," or "controller," or both?
I am assuming that the picture of your accordion's grille shows that a midi controller has been installed. From what I can see it's one of the MusicTech products, although I don't use MusicTech so I can't identify which one it is.
There should also be a connector on the accordion and a cable which leads to a box that supplies power to the controller and to the magnetic contacts for the treble and bass and, maybe, a bellows pressure transducer to send midi volume messages. That box will also have a sound card in it to provide the midi sounds associated with that controller. It will have audio output connectors that will feed your amplifier and speakers, perhaps one or several foot pedal connectors for various functions, and, at least, one connection called. "midi-out", or "ext-out," or just plain "out" so that you can use a midi cable to connect it to the expander. Maybe that's what is referred to as a console?
Now, the second picture is of a Ketron SD-4, which is one of many units that are usually referred to as expanders. These can provide chordal rhythm, drum sounds, and additional midi sounds.
If it sounds confusing, I sympathize completely. Not only is the language used to describe midi setups and their components a little technical, but manufacturer of midi gear A will use the terms to mean something that is different from what manufacturer B will mean by the same term. So tell me, please, what else is included with that accordion and I will tell you if anything is missing. From there, we can go into how to interpret any manuals that came with the components and get you started.