Different things -
'PFI' stands for 'Private Finance Initiative' and 'PPP' and 'P3s' are both shorthand for 'Public Private Partnerships'. PFI and PPP both have very similar characteristics, the key difference being the way in which the relevant project is funded.
PFI involves an infrastructure project (eg a hospital, health centre, school, leisure centre, social housing, street lighting, road or prison) being funded by private sector equity and debt funding and then being paid for by the public sector 'customer' through monthly payments over the life of the project. A PPP project would not necessarily require or have such private sector funding.
A good example of a PPP would be public and private sector parties setting up a joint venture company for a regeneration project, with the parties each contributing one or more of land interests, expertise/people and funding but without any set formula or structure for this.