The knotted lashes are called Flared and the knot free lashes are called Naturals. Sometimes you will see the word 'flare' next to the size of the individual eyelashes (ex. Flare Medium). This only describes the way the eyelash is shaped not whether it is knotted or knot free.

Flared (knotted) have a knot joining the lashes. These lashes offer a slightly better hold than Natural (knot free) lashes because the knot provides more surface area for the glue to stick to. Knotted lashes are also easier to apply because you can see where to position the lashes because of the knot. Ardell Duralash Naturals (knot free) do not have any knots so they do not hold as well as their knotted counterpart, however, Naturals give a more natural appearance and you don't have to compensate for the knot. The knot free end definitely blends in with your natural lashes much better. A beginner may prefer the Flared lashes because you can see exactly where you are placing the knot as opposed to the Naturals which seem to blend in with your own lashes more readily. The end result is the same for both styles, beautifully enhanced, natural looking eyelashes. It all comes down to personal choice and experience.