Whole wheat means the whole grain of wheat is used to make the flour and Whole grain means that the whole grain of whatever grain is used is used to make the flour.
Is this correct?
Yes. Whole grain flour can be made from wheat, spelt, oats, etc. Whole grain flour made from wheat is whole wheat flour.
also whole wheat breads tend to be flatter because the smaller gluten content compared to white breads.
The gluten content is similar, but the bran particles cut the gluten, so it is weaker.
What is a good way to keep the texture and airyness of white but get the healthiness of wheat bread?
Add vital wheat gluten so there is enough to lighten the bread, despite the effect of the bran.
The best 100% whole wheat bread I have ever tasted is this one: http://www.realbakingwithrose.com/2006/11/rose_levy_beranbaums_100_whole.html
Thank you so much for that link to Rose’s 100% Whole Wheat bread, Julie. I just made a 100% Whole Wheat loaf yesterday (using King Arthur Flour’s recipe) and it turned out great (if you’re interested, it’s posted here: http://hanaaskitchen.blogspot.com/2011/01/classic-100-whole-wheat-bread.html). I made some changes, like adding vital wheat gluten but then was told that I shouldn’t have because WW flour is already high in protein. Now I understand better that high protein doesn’t necessarily mean high-gluten (Rose gives an example in TBB regarding semolina flour). Thanks for reminding me that the bran in WW flour weakens the gluten. I will definitely try Rose’s recipe soon!