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 Nomenclature of Peptide Hormones