Can anyone explain...What is the difference between "livery" and "jack" with regards to the Wars of the Roses billmen and longbowmen?

Thanks.

Not a main period of interest so treat this with the caution it deserves!

Troops in "livery" would have a coloured surcoat to show their allegience (based on house or location heraldry) while those in "jack" would have no cover over their armour which would be quilted linen and possibly have metal plates between the layers. Particularly at 6mm scale, the difference between a jack-of-plates, brigandine, gambeson or akheton is largely academic and to do with the methods of construction. They would all be of undyed linen, as linen is all but impossible to dye using medieval methods - at least so I'm told by an acquaintance who's a former wardrobe mistress and with whom I would not dare to argue :-)

So I would expect figures in livery to have a tabard or surcoat while those in jack would have their armour visible.

Livery coats were usually issued to a lord's followers. In the wars of the Roses this might involve the lord, eg Edward IV, issuing livery coats to the troops of the lesser lords supporting him, rather than them wearing their own livery coats. A livery coat was often sleeved. In general they were either one colour, eg. Warwick used red livery coats, or particoloured, usually split vertically, eg Edward IV used murrey ( a deep, wine-coloured red) and blue. Supporters were often issued with their lord's badge as well, to be sewn to the coat either centrally, or more often on the left breast, like a blazer badge. These badges were sometimes also given to men wearing uncovered jacks.  Jacks could also be sleeved. Generally speaking I paint jacks in a variety of buff and pale grey shades with a wash to bring out the lines of quilting. Some medieval manuscripts do show jacks coloured red, blue, green and yellow. To what extent that is artistic license I could not say. Hope this is of some help. If you can get hold of a copy of the MAA Wars of the Roses it illustrates these things extremely well.

As noted, a jack was a form of armoured coat. 

Livery was a sort of early uniform worn by a lord's retainers. Livery would often be worn over a jack.