Is 20mg/g the same dosage as 200mg?

It means that in each gram of ointment there is 20mg of drug.

what medication are trying to measure the mg of. WHy i ask is because take for example OTC pain killer Ibuprofen 200mg is not the same as Acetaminophen 500 or naproxen 330 mg because they are all different groups of medication even though they are all pain killers so they are not the same.

If it's azithromycin 500 mg tablets and the doctor prescribed the 1000mg pack powder and its not in stock the pharmacist can substitute 2 of the 500 mg azithromycin pills instead. Taking into consideration that you have no problem swallowing pills though. In this case its the same drug so the strengths are the same or equivalent.

In your example if you squeeze out 10grams of ointment, then there will be 200mg of medicine contained in the 10 grams.

I think it is supposed to mean 20 mg per each gram.

Not sure what your measuring though, so I could be wrong.