What type of cable runs from the modem, to the wall outlet
They are Coax cables.
The first image shows an isolator, which is used to protect your equipment from surges from your ISP's upstream equipment (the CableModem Termination System).
It incorporates high voltage capacitors to provide isolation to both the inner and the outer conductors of the coaxial connectors
The second image shows a Coax Attenuator, which is used to adjust the signal strength/quality of your internet connection.
This will adjust the incoming signal from the (probably) copper cable coming to your premises to the range required by your Cable Modem.
They will both have been fitted by your ISP when they installed your internet.
You may also have a Cable Splitter somewhere if you also have a digital television subscription.