Earlier quoted context omitted.
In the places I've been, a sysadmin has been someone who operates someone else's product -- not a person operating the systems developers use to operate their own product.
This is my observation as well. Sysadmins writes scripts or small programs for automation but its mostly using those tools for the operation of larger systems developed elsewhere (including other internal depts)
A sysadmin would write the tooling to ensure the payment code could work (failover databases, redundancies) and put safeguards in place so that it does not get traffic that is not intended for it.
Sysadmins used to write the code that touched thousands of machines at once, developers used to write the more complex code which were the bread and butter of the company.
But where I’ve worked, it was never a silo. Just a different mindset, and everyone worked together to do the best they can. That was before “DevOps”.