I had the same confusion as you about these three terms. I called the PTASP Technical Assistance Center to ask for clarification, and the person who helped me summarized it like this:
The PTASP is the rule/regulation (49 C.F.R. Part 673) that tell us to develop an ASP
The ASP is the actual document that our transit agency must develop
The SMS is not a document in and of itself, but an overarching system
The person then added that the ASP documents SMS processes and components, but the SMS itself is not a document. They said there's no such thing as an SMS document.
I had the same confusion as you about these three terms. I called the PTASP Technical Assistance Center to ask for clarification, and the person who helped me summarized it like this:
The PTASP is the rule/regulation (49 C.F.R. Part 673) that tell us to develop an ASP
The ASP is the actual document that our transit agency must develop
The SMS is not a document in and of itself, but an overarching system
The person then added that the ASP documents SMS processes and components, but the SMS itself is not a document. They said there's no such thing as an SMS document.
Hope that helps!