Does a medical discharge in the Reserves work the same way as in active duty?

The hardest part would be proving the condition occurred while you were in a military status.

Firstly, are you still an active reserve? If so, assure your medical concerns are detailed in your medical records now. Simply request your medical records and look them over. If you do not see your concerns noted in your records ask your military medical provider to up-date your records accordingly by scheduling for a full annual check-up that while occurring you assure your concerns are not only being noted but also tests and other methods of medical support are prescribed (seeing a nutritionist for your high blood pressure as well as receiving all other appropriate medical assistance... ) I can't say this enough - make sure your concerns end up on you medical records.
A medical discharge is a specific request informed by your inability to be considered both capable of preforming your assigned task as well as being of value to preform your task - two very different considerations as far as the military is concerned. There are percentages of capability that may vary greatly between an active service member and a reserve service member making becoming designated "in cause" for a medical discharge more difficult to award a reserve member.
Be honest with yourself about your goal toward wanting a medical discharge. This is a significant request and without detailed medical support substantial enough to warrant awarding you will likely not move forward the way you want to. As a reserve you need to assess how your active time as a reservist effects your civilian health and civilian obligations. High blood pressure could come from your civilian life and effect your reservist drill time... not the path you want to go if aiming to be awarded a medical discharge. Pinpoint those medical concerns already in your medical records and assess how they become more distressing due to your time in drill as well as how they diminish your health/capacity as a civilian... a much better approach.
It becomes a bit more difficult once no longer attached as an active or reserve member. However, you do have assistance through organizations such as the PVA and DAV who have service officers available to create service connected veteran medical status for you once no-longer active or in reserve status. I hope this is helpful and am here if you have further questions. Blessings

Maj Marty Hogan thoughts?