A boat is smaller than a ship. We wouldn't say he's traveling to China on a boat...unless it were some herculean task. ;-)
In addition without context, we use the generic "boat". See here:
The Android app doesn't seem to have a way to report a specific example, so I'll post here because it's relevant. One of the four-picture multiple-choice questions has pictures of large ships for both πλοίο (it looks like a ferry) and βάρκα (cargo ship). In fact, the picture for βάρκα is the exact same picture used for πλοίο on the next question.
Yes, you are completely right. We changed the pics to match the boat size. Thanks for the input! ;)