While it's true that Victorian sport bows were mostly ELBs, I wouldn't say that the ELB is strictly a Victorian sport bow.
The name derives from the bows used by the English in battles between the 14th and 16th century. The EWB has several distinctive characteristics. The only examples available to us are those from the Mary Rose and thus the English Warbow Society defines a warbow as one that is 70+ pounds at 32 inches at the very minimum and at least 72 inches in length. The bow is tillered full compass, meaning that it bends through the handle and the arc is more circular than elliptical. The belly is rounded and the dimensions follows the 5/8ths rule for depth/width throughout the bows limbs. While period warbows were most often yew, other woods were also used and today laminated woods are accepted. Warbows are not to have unnatural reflex though heat/steam straightening are acceptable. Adding a leather grip doesn't negate it being a warbow as long as it bends through the handle.
Basically, if you make a bow and it meets that criteria, then you can probably call it an English Warbow and not get your head chopped off.
The English longbow is similar in most ways such as the 5/8ths rule, but could be less than 72" (but not by much as it is still a "long" bow), less than 70 lbs at 32 inches, and can have a non-bending fat or raised handle. Given the non-bending handle, the tiller will often be more elliptical.
On a side note, though not technically a part of any definitions I've ever run across, both the ELB and EWB most often have horn nocks. Most horn nocks seen today are shaped with the string groove cut across the back, but evidence from the Mary Rose clearly indicates that the nocks all had the groove on the side.
