In a project I’m working on I needed to post a message from a C# exe to a window in a Clarion dll. I thought, like you, that they were equivalent and I could find the msg code for POST and/or NOTIFY. After testing and analyzing subclass message logs, I couldn’t find anything. Then I found this post where Alexey explains that they are different things.
I ended up using PostMessage from C# and a Clarion subclass procedure to NOTIFY the window.