Possibility of being compensated and or benefits
Before I answer the question, it is important to understand that the term "medical discharge" covers a range of different outcomes from the Physical Disability Evaluation System (PDES). You can have Separation without Benefits, Separation with Severance Pay, Temporary Disability Retirement, or Permanent Disability Retirement. I think your friend would most likely fall under the separation with severance pay scenario, but I am going to spell out all the different possibilities in case anyone else is curious.
The most important difference that I can think of between a regular discharge and a discharge as a result of referral to PDES is the possibility of receiving compensation and or benefits. Remember, though that under current law, unless the servicemember has 20 years or more of service and is eligible for concurrent receipt, he will have to offset his VA payments dollar for dollar against his military disability compensation. For example, if he is awarded $20,000 from the Navy PDES and is later awarded $1000 a month from the VA, he will not receive a check from the VA for 20 months, until he has "repaid" his VA offset.
If found unfit solely due to a condition that existed prior to service (EPTS) and was not aggravated by military service or a condition that was the result of intentional misconduct or willful negligence, the outcome is separation without benefits. This would mean little difference between a separation due to expiration of enlistment contract and being discharged in this scenario.
If found unfit due to a condition (or conditions) that was (were) incurred while entitled to basic pay or was EPTS but aggravated by military service and rated using the Veterans Affairs Schedule for Rating Disabilities (VASRD) at either 0%, 10%, or 20%, you would be entitled to severance pay. This is calculated as 2 times years of service (but not more than 12 of those years) times base pay. So depending on years and pay, this can be a substantial amount of money.
If found unfit due to a condition (or conditions) that was (were) incurred while entitled to basic pay or was EPTS but aggravated by military service and rated using the Veterans Affairs Schedule for Rating Disabilities (VASRD) at 30% or more, but those conditions are found to be unstable for rating purposes, the outcome is being placed on the Temporary Disabled Retired List (TDRL). On TDRL, you are in a temporary retired status- you receive a minimum of 50% of your base pay and you get the same retiree benefits as a length of service retiree (commissary, PX/BX, and medical benefits). You can only remain on TDRL for a maximum of 5 years. While on TDRL you will be re-examined periodically (usually around a year to 18 months) to determine if you have stabilized. After the re-exam, you can be found fit, unfit and separated without benefits, unfit and separated with severance pay, retained on TDRL, or placed on the Permanent Disability Retired List (PDRL).
If placed on PDRL, it means that the Board found you unfit for stable compensable conditions rated at 30% or more. That means that you are permanently retired and you receive the higher of your rated percentage under the VASRD times your base retired pay or 2.5% times years of service. It also means that you get the same retiree benefits as a length of service retiree (described above in TDRL).
Like I mentioned earlier, your shipmate is most likely looking at severance pay if he is found unfit (given that back pain seems to be his only conditions). If you had to sum it up, the main difference is the possibility of being compensated.