My surgeon told me he could take me from a 38D to a 38B. Is that because my band is a 38?

You are correct- the number part of a bra size refers to the circumference of your chest. This may change with weight loss or gain, or if you have liposuction under the arms. But just having a breast reduction does not change the number. The actual cup size is the difference between your bust measurement and your chest measurement. A difference of 1" is an A cup, 2" is a B cup, 3" is a C cup and so on. I always tell my patients that I cannot guarantee a specific cup size after surgery, because bras all fit differently depending on the manufacturer. Instead, I have my patients tell me whether they would still like to be a little full (generally in the D-cup range), proportional to their frame (usually a large C to small D), or as small as possible (around a B cup). Best of luck with your reduction!

Yes, I think you have a good understanding. However, be careful about communicating your goals in terms of achieving a specific cup size. As you know, cup sizes may vary from one bra manufacturer to another. In my practice, I ask patients to avoid communicating their goals and/or judge the outcomes of breast surgery utilizing cup sizes as a reference. Instead, I find the use of goal photographs much more helpful. Best wishes with your upcoming surgery; this operation tends to be one of the most patient pleasing operations we perform.

Yes, you are correct. Typically the bra size change after breast surgery relates to the cup size (letter) and not the band size (number). The band number is the distance around your chest and ribs just below the breast crease and remains the same.  

You are correct, the back size will not change.  The volume of the cup will in a breast reduction. Best of luck.

Yes, in general your band size stays the same when you have a breast reduction because the tissue is coming from your breast area, and the band size measures the length around your ribcage under your breasts. Sometimes patients choose to undergo liposuction of the under arm area at the same time, so this can potentially decrease your band size as it removes some of the fat in the area that is measured in your band size.