A wild flower is not necessarily a weed. The bluebells in spring, the red campion later and the angelica in summer are all wild flowers but in the right part of the garden are not weeds.
However there are some that I classify as weeds wherever they are - especially the tenacious ones - Bindweed, Ground elder, brambles and hogweed. Now some people seem to like the majestic white panicles of the hogweed but I have been blistered by the sap! So I much prefer the white flower heads of the Wild Angelica.
Grass is grass but in flower beds couch grass is weed. Add to this clover and creeping buttercup, cress and oxalis, dandelions and docks and so on.
This is persicaria- related to Easter Ledges (still have not cooked them a la Mrs Beeton) - and redleg. It grows on the banking above the pond and makes a fine display. Weed?
Then in gravel paths everything is a weed though you can transplant some self sown seedlings like wallflowers and aquilegias.
Early on I put in some ground cover roses for a quick result and have certainly got it. Now they are rampant and need a strong hand.
The ash, willow and sycamore trees self seed - definitely weeds in the beds. Raspberries sucker and come up where they are not wanted - the list is endless.
So weeds are only weeds if they are growing in the wrong place - especially brambles.
Mind you, they do have juicy blackberries . . . .