"When & how should you use a BPM tool"
Oscar Reyes makes the point directly in the first sentence of his post. You need process vision.
A BPM tool (strictly speaking), is a tool that's supposed to manage business processes. The warning in Godeke's post above is also right. Not all BPM tools are created equal. In fact, I challenge you can't get anyone to agree on what BPM actually is. The term has been usurped by various parties including software vendors, consultants, analysts, and news organizations (to name a few).
But to answer directly, a BPM tool is appropriate when a business wants to automate a portion or all of a business process. Note... all businesses have business processes. It's just that not all businesses document or manage by them.
'How' to implement a BPM tool is context dependent because there are different 'types' of BPM solutions. Broadly speaking (and this is fodder for debate), you can break down BPM into transactional and human-centric processes. Transactional BPM is targeted at automating system-level processes - mostly integration. You'll see lots here about SOA. Human-centric BPM is targeted (obviously) at processes that involve human interaction - mostly document or structured/unstructured data management.
"differentiate Business Process from Application Workflow"
See above. This is a very generic discussion. And much needs to be done up front to adequately identify a BPM project.
The first question to ask is, "Does our company currently manage its business by process or does it want to?". The answer to this question should come from the top. My experience has been that without the executive-level commitment to process-centric business management, a BPM project will likely fail to meet its objectives. Not that you won't be able to install a BPM tool and get it to integrate systems or manage electronic documents, but that the ROI of the project will likely be missed or lost.
Bottom line, a BPM project will require a process-centric business vision, and with that, you will be in a much better position to define an appropriate architecture to support that vision.