Well, really a weed is just a plant growing where we don't want it...
I try to be pretty diligent about cleaning out the weeds in my vegetable garden but always have some interesting volunteers (lots of bird-planted sunflowers, and things that self-sow like dill and amaranth - which are easily recognized when small so I let them be). My often-neglected flower garden, on the other hand, has much more of a chance for volunteers (both flowers and weeds) to grow