Major commercial species included in the white oak group are white (so this is a bit confusing), chestnut (leaks if used for liquid barrels), post, overcup, swamp chestnut, bur, chinkapin, Oregon white, and swamp white (really hard to dry swamp white without checks).
Included in the red oak group are northern red (often just called red, so a bit confusing), southern red, scarlet, Shumard, pin, black, cherrybark, water, laurel and willow.
Live oak is indeed a white oak, but its properties (including density, strength, interlocked grain, evergreen) are quite a bit different than the other commercial white oaks, so it might be best considered separately. Actually, there are several important species called live oak; they are all similar in properties.
There are around 20 commercial red oak species and 20 white oaks. A dendrologist might find that in North America we have over 100 species of oak.
For the most part, the species in the commercial red oaks are quite similar and also the commercial white oaks, so from a practical point of view, we do not separate them within a group (except live oak and sometimes California black oak). However, we do separate the oaks within a group into those with rings spaced about 1/4" or more apart from those with closer ring spacing. The wider spacing (sometimes called Southern, but not too accurate) is harder to dry, a bit more dense, and higher shrinkage, with some resulting processing differences.
Also, those oak trees with anaerobic bacterial infections will produce drying and strength issues. As the bacteria are more common in wet sites, and some oak species prefer wetter sites, we see more issues with the wide ring (Southern) oaks. As the species listed above are often found in one region of the country (northern or Appalachian, for example), we often say that one species is harder to dry than another, but it could be due to the higher risk of bacterial infection and not the wood itself.
Assignment writing structure: Look at tree or log quality factors (straight grain, growth rate, knots, color, shake or odor, sweepy log, etc.) rather than being overly concerned about the species within the white or red group.
.....buy and prefer Live oak......they say it burns hotter longer.....but it tends to smoke very heavy if not seasoned well.......and the Post oak I have been using burnes good and fairly clean after the initial fire starts.......My favorite is Black Jack oak, but hard to find in North Central Tx........IMHO for Comp bbq the post oak is a msmoother milder smoke for most judges palates.... 
