Wild plants are those plants that have evolved without without human interaction. Actually, that is not true at all. A lot of them rely on humans for spreading their seeds - the best example being plantain that was spread by European colonists on the American continent. The sticky seeds made the long travel on their shoe soles and spread everywhere they walked - it gave plantain the name 'white man's footstep'.
But what I mean is that they have not been cross-bred or cultivated for various reasons: bigger or more colorful flowers (like roses), bigger fruits (think strawberries), less bitter leaves (like wild lettuce). But a wild plant is not by definition a weed. Native orchids are wild plants, and so is arnica, or common sea-lavender. And they are not growing like weeds - they are rare, and often protected.
A weed is a plant that grows abundantly in various circumstances. It's not picky about the place where it grows, or the soil, it's not vulnerable to diseases or plagues. It thrives under extreme conditions. Even some cultivated plants may grow like weeds, though most of them are wild plants. And generally, they love the company of humans. You find them in greater number in cities, gardens and meadows (yes, of course the countryside is a cutivated landscape) than you'll find them in the deep wild (or whatever's left of that).
They are very adaptable. Pictured above is broad-leaf plantain, and it shows the potential of weeds to adapt to their environment. Both leaves were picked only 1,5m away (that's about 1.6 yards), and yet their size is significantly different. The leaf on the left side was growing in the shade. This plantain plant made huge leaves, in order to increase its surface. Why? Photosynthesis.
The leaf on the right was picked from a plantain that was growing in a sunny spot. It had lots of sunlight, so had no need to form a bigger leaf. This is plant language, folks. This is how you can read where a plant has been growing.
Keep in touch - more about plant language soon!