The essential difference is in the draw-weight and later, in the draw-length.
Also in the style of tiller.
Also target weight "lawn archery" bows of the gentry in the later period were often made of joined billets and had a different tillered shape.
The "war bow" is really a single stave and fully tillered, every part of it's length doing some work, even if only slightly bending at the handle and tips.
There is a benefit in distributing work of the greater load over the full length of the stave.
The lawn archery bow in it's later forms very often, particularly in a joined "billet" bow, had a stiff handle and relatively stiff tips.
In this style the work of the bending limb is distributed over a smaller proportion of the stave's length.
Also the cross section came to differ considerably, particularly in the very slender low weight bows made from tropical hardwoods.
These often have the "high arched" section that is all too often mistakenly given as the archetypal English bow section, which it is not really.
The heavy single stave bow is usually more rounded out in section, which is functional in terms of better distribution of stress that would be concentrated in the corners of a more exaggerated profile
.
Hope this helps.
Rod.
