The difference between homegrown and medical

is that “homegrown” is grown at home and “medical” is of or pertaining to the practice of medicine.

homegrown

Grown at home.
Created or constructed in an informal or amateur manner; done without formal assistance, as from a business, organization, or professional.
Raised or brought up in one’s own country.
Originating in one’s own country.

Each spring they planted a garden and each summer they enjoyed homegrown vegetables.
The design, though homegrown, was robust and well planned.
One had never stepped in a rowing boat until 2008, the other will return to serve in the Royal Artillery in September. But Glover and Stanning will now go down in the record books as the first homegrown gold medallists of the London 2012 Olympics.
As historian Paul Hanebrink writes, the far-right in Europe could not accept that the success of the 1917 Russian Revolution represented genuine homegrown support for leftist politics, so communism had to be explained as part of “a Jewish plot to overthrow civilization and impose foreign rule on the nations of Europe.”

medical doctor; medical student
Do you have any medical experience?
The US supreme court has ruled unanimously that natural human genes cannot be patented, a decision that scientists and civil rights campaigners said removed a major barrier to patient care and medical innovation.
medical marijuana; medical cannabis; medical treatment
A costly medical condition can bankrupt you if it doesn’t kill you first.
medical examinaton; medical exemption; medical history; medical record; medical diagnosis
medical ward

You’ll have to get a medical before you apply for that job.
After completing a medical and the requisite paperwork on Tuesday to seal the deal, Di María said: “I am absolutely delighted to be joining Manchester United. I have thoroughly enjoyed my time in Spain and there were a lot of clubs interested in me, but United is the only club that I would have left Real Madrid for.