For ESA, a claimant cannot be found 'fit for work' without a face2face assessment so this letter would be indicative of a positive decision. I would expect a decision letter to arrive within 2-4 weeks from this point.
For PIP there is no such constraint, so this letter simply indicates that the assessor felt they had enough information to recommend a decision. It is taking around 8 weeks in many areas to get a decision letter once DWP have the claimant's file back.
Nothing on this board constitutes legal advice - always consult a professional about specific problems