The terms accordion shutter is frequently used to describe a interior shutter unit that uses panels that hinge together. An accordion interior shutter unit would attach two or more panels together so they open in the same direction. The outside panel would hinge to the window jamb or to a hang strip directly outside the window opening. When fully open, the shutters all stack (front to back) to create maximum visibility through the opening. A bi-fold shutter unit would only attach two shutter panels so they would fold in the same direction.
Accordion shutters is not the best phrases to use when describing a folding shutter unit. Instead, refer to the number of shutter panels across and how many panels hinge and open to the left side and how many open to the right. An accordion bi-fold shutter unit with four panels across usually open two panels to the left and two to the right. An accordion shutter unit with six panels across usually open three panels to the left and three to the right. It is possible to hinge all panels together and open them to one side.
Accordion doors or doors are often used to cover interior closets and pantrys. The accordion doors open to the side of the opening allowing entry to the contents.
Some local shutter companies that measure and install shutters will tell you that they are "certified installers" to discourage you from attempting to measure for and install shutters yourself. Most likely they certified themselves or attended a one day training session with their supplier. With proper instruction, homeowners are fully capable of measuring and installing shutters themselves.