A protégé is literally a "protected one". It is used of a younger person being being developed under the guidance of an experienced older person. It is a French term.
The younger person might be seen as an apprentice, and the older person as a mentor. If it is a physical activity, such as sport or dance, then the formal term might be 'trainer'. However, the term is not formal or official. It is just a way of describing a relationship. Psychosocial support and career guidance come into it, but usually not money.
So the relationship is informal, but often important for the protégé.