So I'm playing on the Bog on my Xbox and I'm trying to try crane loading with the C-375 truck, but as I load as many logs as I can fit on the medium cart and verify all the logs have green dots, I leave and go to the lumber mill, but when I arrive it says I have no load. I remove the red dot logs, or fix it, and it still says I have no load when I have about 18 or so logs. Is their something I'm supposed to pack it or strap the load in?

You have to pack the load. You actually don't need to load the trailer at all, only a few logs. Here is the requirements for packing.

Short logs - You need to load 4 (optional you can load more if you want, but you don't need to)

Medium Logs - You need to load 3 (optional you can load more if you want, but you don't need to)

Long Logs - You need to load 2 (optional you can load more if you want, but you don't need to)

Once you have the required amount of logs, select your truck you want to pack a load in, start the engine, make sure the truck and/or trailer is on relatively level ground, and just use your d=pad and lick through options until it highlights your load, then click the button to pack.

Skip to 02:06:00 to see what I'm talking about, I load and pack 2 loads of short logs.
Youtube Video

I remember going through something like this when I was new to the game. The game should have a tutorial on log packing.