There are multiple ways to do this (as is typical of SmartThings).
First, here’s the custom code FAQ–that might help clear up some of the confusion regarding smartapps vs device type handlers.
Second, you may be overcomplicating this. Ring has an IFTTT channel. SmartThings has an IFTTT channel You can already have motion detected by Ring trigger a SmartThings event that way. You don’t need to use any other channels.
If you are unfamiliar with IFTTT, the following is a good tutorial:
One of the things you could have IFTTT do is turn on a virtual switch in SmartThings. Then you can have that switch trigger all kinds of events within SmartThings. If you don’t know the simple way to create a virtual switch, here’s the FAQ for that.
But suppose what you really, really want is to have something register as “motion detected” within SmartThings?
This is where it gets really fun. Mike Maxwell has created a universal device type handler which can make one kind device report as though it was a different kind of device. So you could have your simple virtual switch report as a motion sensor! Which is, of course, awesome.
So there you have it:
A) just use IFTTT to have motion detected on the Ring cause a single event in SmartThings
or
B) use IFTTT to have motion detected on the Ring turn on a virtual switch in SmartThings and have that virtual switch coming on cause other things to happen in SmartThings, like maybe a mode change or a light come on or both.
or
C) use IFTTT to have motion detected on the Ring turn on a virtual switch in SmartThings which, through the use of @Mike_Maxwell 's universal virtual device type handler can then appear to SmartThings to be a motion sensor.
Your choice.
Also, for any of these you could use that single ring motion detected as the “IF” in multiple IFTTT recipes if you want.
There are other ways to do this as well, but these are the simplest, I think.