In Wisconsin, where I go fishing every year, it's pretty easily stated and well known up there. A cabin, weather on a lake or in the woods is usually meant to be a log cabin or at least a dwelling built mostly of wood. They have what they call cottages, which is meant as a dwelling, built like a normal house, but usually meant for 3 seasons as they are built on a raised foundation and usually don't have the means to heat the water supply during the winter. Then there is a lake house. These are your typical homes, built on a lake.
At the very least, if you call something a cabin, it should definitely have that woodsy, "cabin" feel. Other than that, it's just a lake house. I have a friend who's family have both a cottage and a cabin. They call the one a cabin and the other the cottage, because the cabin is an original log cabin from the early 1900s built as part of a resort, the cottage is just that, a house on a raised foundation they close down during the winter.