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Bifurcators need not be divergent pieces any more than divergent pieces
need be bifurcators.  George Jeliss brings forth 5 bifurcators from
20th-century problemists in ''All the King's Men'' none of which are
divergent [though that glossary is currently unavailable to confirm]. Western Pawn and Eastern Cannon are classically divergent and
they are not bifurcators.  13th-century
Gryphon is bifurcator and not divergent; it takes re-interpretation of Gryphon that cannot stop on the first square to fit this convenient example of the oldest pure bifurcator.  ''Divergent'' just means capture and move are different from each other. ''Bifurcating'' just means splitting into two directions to choose after starting in one other original direction. That more specified means diagonal, then either of two available orthogonals; or the vice versa.  Winther's 30 or so bifurcators, including Jeliss', have both modes, some one and some the other, in many Winther bifurcators' also being divergent.  To simplify, Winther appears to have been removing the divergent aspect from some bifurcator move-definitions. As of now, one particular bifurcator the Crossrook ''slides like a Bishop. It captures by jumping over one piece.'' Similarity of capture-modality to Dawson Grasshopper is noted. That makes the piece-type divergent, since there is no capture along the first-leg diagonal before the screen. If the square jumped-to is empty, the continuation is 45-degrees orthogonally either of the two ways.  That makes the piece-type bifurcator. 
http://www.chessvariants.org/index/msdisplay.php?itemid=MLcrossrookchess.
Winther means to allow capture along the second leg too instead of screen-jump location if there is chosen continuation. There is too defined by Winther a weak interpretational Crossrook dis-allowing capture at the jumped location. Now this one piece-type can have really, not just the two, but 5 or maybe 10 sub-piece-types whilst staying the same basic bifurcator. What makes it Crossrook at core is ability conferred by another unit to jump over along a diagonal from a starting square with the next square vacant or foreign and possibility of bifurcating continuation.  The  afore ''foreign'' would imply Winther's strong Crossrook interpretation. Now the same type conceivably could permit variably: (a) capture first leg too; (b) capture only one of the orthogonal continuations, either the left or the right; (c) no divergence, meaning no stopping at all the first leg; (d) double capture of the enemy both right beyond the screen and also along a second leg; (e) mandatory bifurcating continuation without another capture allowed after a first-leg jump capture.  That makes 6 or 7 different Crossrooks who are still bona fide, staying very distinguishable from the other 30 bifurcators such as Venator, Crossbishop, Dimachaer.  (Also more or less off the cuff, I did this before for multi-path Falcons, making up to ten different piece-types in ChessboardMath6,
http://www.chessvariants.org/index/displaycomment.php?commentid=22662, who are all one and the same core Falcon of multiple routes and same destinations.)