Hi Pamela,
Its very simple:
Avail. Chk - To check the status of the stock position for your material.
Depending on the Scope Check maintianed in the availability settings (OVZ9 t-code).Meaning, based on the factors that you would like to check for the availability of the material and it will not impact the stock position - It will just give you INFORMATION on the stock.
TOR: Whereas TOR would help in integrating with other Modules. It share the information that there is a requirement and hence please make sure you (MM/PP) arrange for the same. MEaning it will have impact on the process, like procurement / Production activities can beinitiated based on the sales order requirements.
Please let me know for any further calrification - would definitely help you.
regards