If you measured 37 inches around your chest right underneath your breasts, and you measured 40 inches around the fullest part of your breasts, that would be a 38B. You may want to used this calculator to see if you indeed are a 38B. Remember that measurements are a starting point. Shape and style bra along with measurements will get you to where you need to be. You may want to use the six measurements this calculator uses to get a more refined measurement.
https://abrathatfits.org/calculator.php And don't get hung up on the numbers and letters. That is the number one reason 80% of all women wear the wrong size bra. Band size to cup size is a ratio. A 38B is the same cup size as a 32DD. An A cup is 1 inch larger around the fullest part of the breasts over the band. B is 2 inches. C is three inches, etc. In the end it is all about comfort and support, not numbers and letters. The band should be sung, but not uncomfortably snug. 80% to 90% of support comes from the band not the straps. For this reason is why you need to have to band snug. Nothing red or angry. It will leave a mark on your skin but it should fade within 30 minutes or so.
For most men, if you are looking at an underwire, which gives the best support and shaping, you are looking for a plunge bra. Most men are wide set, meaning their tissue is such that you can put two or three fingers between the breast and are shallow in shape meaning there is not much tissue above the nipple. Underwire plunge bras work well for this shape. One thing to remember with all underwire bras is that the gore, or the bridge part between the breasts should tack, or sit flat against the sternum with each breast separately encapsulated in each cup for best support and comfort. Soft cup bras or bras with no underwire will not lay flat. Not enough structure to force the gore flat. Soft cup bras also have a tendency to give a mono boob look but are very supportive and can be shaped due to the use of stitching on and around the cups. Stick to skin tone colors. White has a tendency to outline through other clothes. Your breasts should comfortably sit in the wires of the cup if underwire. Any pinching or other discomfort or what is called "quad boob" or tissue trying to escape over the top of the cup is a sign the bra/cup is not the right size. The cups should smoothly encase the breasts with no detectable bra lines. Bras are an external form fitting skin with built in scaffolding to support tissue that has no support structure of its own. And always when putting on a bra, lean forward, let the tissue naturally fall into the cups, then scoop all the tissue under your arms into the cup before standing. This is called "swoop and scoop." Some women don't do this and this is why they complain about fit and comfort. Tissue goes back farther than most people think. Getting all this tissue in the cup helps with comfort, support and appearance. I normally wear my bras 15-19 hours a day, every day and forget I am even wearing it most of the time because I am wearing the correct size bra and I swoop and scoop when I first put it on. And bras are a try it on thing. Very rarely do you get it right the first time, or second time or third time. It's the nature of the beast. You keep trying on bras until you find one that works. This is because no two breasts are the same. Not even on the same body.
Good luck!