A definition of charity - from wikipedia.
The practice of charity means the voluntary giving of help to those in need, as a humanitarian act..........so Macmillan
A charitable organization is a type of non-profit organization (NPO). It differs from other types of NPOs in that it centers on non-profit and philanthropic goals as well as social well-being (e.g. charitable, educational, religious, or other activities serving the public interest or common good)...........so CRT
There IS a difference, and many people, when they see the word 'charity' think of the Macmillan example rather than the CRT example.