The difference of right or left is partly secondary. More right hand cut cemented bits [AR] are sold/ used/ on hand, kind of determining why fly cutters are also right hand cut, like endmills, drills, reamers and most everything else.
But I find left smaller left hand [AL] on sale every once in awhile...so here is my spin on flycutters.
They are slotted as shown on the drawing, perpendicular to holding spud at about 1.75-2.0x deeper than tool is square. Every so often I add a set screw perpendicular to slot, a 'jack' to maintain cutter incline angles. Instead of set screws as bit holders, regular socket cap screws, with customization in length make a hex easier to find. Also flat tips make tool projection simple to adjust, compared to the divot from cup points.
I think your right hand/ left hand question bears on orientation in the slot. Either way the side cutting needs the front and side clearance to operate; just like a lathe tool.
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