We’ve hunted around for a definitive answer since you first wrote, and finally asked a travel agent for her thoughts. But this is a pretty gray area, as you’ll find some variation from country to country, from hotel to inn, from bed & breakfast to pension, and - most important - from the brochure of one travel company to that of another.
A Continental breakfast traditionally is bread or rolls or croissants and butter and perhaps jam, with coffee or tea or hot chocolate. Not only is that a Continental breakfast, it is full Continental breakfast, the "full" having been added to make the trip sound even more wonderful and therefore worth any amount of money.
Some countries on the Continent, such as Holland and those in Scandinavia, add a bit of fruit and/or cheese to the bread menu, occasionally even a boiled egg or a little salami. In Britain, of course, breakfast can include bacon, eggs, toast, a bit of broiled tomato, etc. We’ve heard that referred to as a full English breakfast.
But the full European breakfast sounds to us and our travel agent friend as "marketing fluff."