What is the origin of the suffixes "statin" and "medin"?
Much of the terminology in medicine is from Latin, some from Greek, and in extremely rare instances, it's made up (usually initially as something humorous.)
-Stat comes from the Latin stare (statum), meaning:
remain, rest; stand, stand still, stand firm
The use of -stat as a suffix usually means that it will make something come to rest, to stop, to stand still.
Hemostasis is the act of stopping bleeding. A tool to clamp a blood vessel is called a hemostat. A bacteriostat stops bacteria from replicating, in contrast to a bacteriocide, which kills the bacteria. Statins are so named because they interfere with (stop or cause to come to rest) the production of cholesterol in the liver.
Somatostatin is a hormone that stops others from being secreted. The -in ending is added because traditionally peptides end in -in. For example, insulin, lactoferrin, hemoglobin, immunoglobulin.
-stat is a very common suffix in medicine.
-Medin comes from the same rood as mediate, the Latin word mediāre (past participle: mediātus), to be in the middle, to intercede, + -in (it's also a peptide.)
A hormone which intercedes (or up-regulates) something else can have the suffix -medin. Somatomedins are hormones that promote cell growth in response to stimulation by growth hormone. It acts as an intermediary, if you will, between a hormone (or step in a reaction) and an effect.
-medin is not a very common suffix in medicine.
The Somatomedins
The Nomenclature of Peptide Hormones
(This should probably a comment and not an answer, and in fact might be more at home in the HSM site than the English one.)
For the HMG-CoA reductase inhibitors (the cholesterol-lowering drugs), the first member of the series, lovastatin, was originally named mevinolin by its discoverers at Merck1, and monacolin K by researchers at the Japanese company Sankyo2. The renaming to the USAN "lovastatin" was apparently at the behest of the FDA, and all of the succeeding HMG-CoA reductase inhibitors followed suit with the suffix -statin. Note also the topical antifungal drug nystatin, apparently named after "NY State", but bears no relation to somatostatin or the HMG-CoA reductase inhibitors.
(P.S. I was a pharmaceutical chemist in a former life.)