It not only depends on the ship, but also on the port. Some of the ports are only designed to load from the side, others like Bellingham and Prince Rupert load from the bow or stern. They haul many large truck trailers to deliver goods to the different communities. As Ron says, they will take good care of you and your vehicle on the ships.
Here is the Malaspina loading in Skagway and it uses a side load at that port. We are talking serious sized ships in the AMH System.
A couple of more photos on edit: This is at Prince Rupert, where they back the Big Mat in stern first and load straight into the stern. A small side issue is all the AMHS fleet operates on Alaska Time, even though when in PR, they are in the Pacific time Zone, the ship still runs on Alaska Time. LOL
They have you line up in the parking lot based upon size, type, destination, etc. Then the load master off the ship, decides which vehicle goes on next. The couple is walking up the loading ramp as all the off loading vehicles are already off the ship.
We were going straight through from PR to Skagway, so we were loaded last. So when we arrived in Skagway, we just drove forward the length of the ferry, and turned right, to drive out the very large side cargo door, then up the ramp to be on our way.