Note: these are my notes, they may well be incorrect. Knapweeds are best identified from a side-view of the flowerhead, which shows clear details of the phyllary bracts (green or brown overlapping "scales" at the base of the "flower") Most common in central NJ (my area) is C. nigrescens, Tyrol knapweed. Each bract has a larger green triangle at the base, with a smaller, dark (black or brown) roundish disk on the end, which is fringed with 5-8 bristles on each side. The green triangle never has bristles outside of the disk. The disc does not obscure your view of other bracts.
Most common in NJ as a whole (and especially in the coastal plains) is C. stoebe, spotted knapweed. Each bract is triangular shaped with length-wise stripes and a dark border on the upper third. This dark border has bristles. Also, the basal leaves are very divided, moreso than in other Centaurea species.
I don't have a photo of it, but batchelor's buttons, C. cyanus supposedly is a common escape in NJ. It has bright blue flowers with very broad ray flowers, a very different color from any other of the knapweed species.
Brown knapweed, C. jacea has larger flowerheads than either Tyrol or spotted knapweed. It's bracts are brown and papery, not triangular-shaped. They can be somewhat bristly at the base of the phyllary, but near the "flower" they are not and are often notched. They are not green, not striped, and not narrow.
Black knapweed, C. nigra, is not often seen in NJ. It's bracts seem to be all fringe. They are very narrowly triangular and obscure the bases of the other bracts. They have more than 8 bristles on a side.
There is a hybrid of brown and black knapweed, Monckton's knapweed, C. moncktonia. It has strongly fringed lower bracts and papery, notched upper bracts. I believe this is it here:
Finally, there is the garden flower, perennial coneflower, C. montana. It has blue ray flowers that are extremely narrow and widely spaced. I don't believe it escapes:
