|Im thinking the printer needs to be either connected by ethernet to the cable modem or wirelessly to the cable modem but not both.|
Correct. If you tried to connect it to both, you'd likely give the printer a headache and it would stop working altogether.
Or the wireless devices can print wirelessly to the printer without going through the cable modem.
If the cable modem is also a wireless capable SOHO Router, and you've created your wireless network on the router, and your wireless printer is connected to the wireless network you created, then yes, print jobs will go through the router.
I'm not sure why this is an issue. It's a difference of a few milliseconds at best in the time it takes the print job to get to the printer.
Which would be faster?
"Faster" is relative. For the average print job, there would be little, if any, discernible time difference in how long it takes the print job to make it to the printer. I suspect it would have to be an incredibly large print job before you'd notice it getting to the printer "slower" via wireless than wired. I'm talking a big data package, as in Gig's of data, not just a few kb's or even Mb's
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.