What is the main diference between Red Crescent Society and St. John Ambulance?

One key difference between the two groups in the concept of membership.

St. John Ambulance is a common name used by a number of affiliated organisations in different countries dedicated to the teaching and practice of medical first aid and the provision of ambulance servicesall of which derive their origins from the St. John Ambulance Association.

Each national group falls within the charge of a Priory or National Council of the Venerable Order of Saint John in which each Priory ranks alongside the others.

Most members of St. John Ambulance are not themselves members of the Order.

Red Crescent Societies are humanitarian institutions, part of the International Red Cross and Red Crescent Movement.

Currently 186 National Societies are recognized by the ICRC and admitted as full members of the Federation. Each entity works in its home country according to the principles of international humanitarian law and the statutes of the international Movement. Depending on their specific circumstances and capacities.

https://en.wikipedia.org/wiki/St._John_Ambulance

https://en.wikipedia.org/wiki/International_Federation_of_Red_Cross_and_Red_Crescent_Societies

Adding to BRY2K's answer. Red Cross Red Crescent are the societies that go in during natural and man made disasters to help the most vulnerable. Each "sister society" works within their country according to what is mandate for them through governments and other NGO's (non governmental organizations. They also respond as requested to other countries during time of war and disasters. They also send monies to the ICRC and the IFRC to help with the disaster recovery and preparation in other countries. Both are volunteer driven with with minimal paid staff.
Red Cross also teaches Water Safety, RespectEd programs(abuse prevention) and disaster preparedness programs.

Source: I work for Red Cross

http://www.ifrc.org/

http://www.redcross.int/

[Links added -- Zb]