Cottage Garden design themes have evolved for sure, especially in American gardens. Early, traditional cottage garden designs typically had a somewhat formal structure they way the paths were laid out in straight, symmetrical grids and often edged in short boxwood or herb hedges, but the garden within was less structured with plants meandering together. Originally they were the result of the gardener having very little space to work with, and maximizing use of that space. In American home gardens, we often have more space to work with, and have the freedom to pull from traditional cottage garden design concepts that work for us individually. Early cottage gardens, being small, typically had no lawn space, but most cottage gardeners in this country maintain lawn space as well. The paths and borders in my garden are serpentine and flowing, following the lay of the land. While that isn't a traditional cottage garden design, the beds themselves are planted in a cottage garden style, and the informal borders work well with the meandering plantings within.
I think the traditional English cottage garden often blended the formal with the informal, like a neatly trimmed topiary among the informal plantings. I find that unexpected blending adds nice visual interest. That's one of my favorite aspects of the English style of gardening in general.