RTF - Registered training facility - provides training for Private Pilot Licence and Night Qualification (and in the UK, IMC Rating).
As the name implies the only requirement is to register. Applications to register are free and will not be rufesed unless the authority considers that the propsed facility will be unsafe or unable to complete the required trainng.
FTO - Flight Training Organisation - Must be approved to complete various courses - Multi Engine Training, Instrument Rating Training, Commercial Pilot training and/or ground training. There is a sizeable fee for the approval process which must be renewed on a regular basis. The requirements are clear with regard to accomodation, facilities, aircraft, operations and training manuals as well as appointment of staff, conduct of courses and assessment of students.
If an FTO wants to also complete PPL training, it will register as an RTF for that purpose.
Thus from a student's point of view, there should be little if any obvious difference. Most importantly, the authorities make no comment available as the the financial viability of any FTO and thus if a student pays up-front, for a PPL course, there is no extra protection in going to an FTO as opposed to a simple RTF.
From an instructor's point of view, what they can teach is determined by their ratings and experience. Thus a FI(R) working for an RTF will teach the exact same parts of the PPL course as an FI(R) teaching at an FTO. However, as the FI at an FTO gains ratings, they can with certain experience qualify for teaching of the CPL flying phase or with a multi engine instructor rating can teach multi engine ratings and so on.
Thus overall from an instructor's point of view, the teaching will be the same but progression can be easier if the organisation is an FTO.
Hope that answers your questions.
Regards,
DFC