Afterschool or Afterschool?

I saw a banner fluttering on a neighborhood apartment yesterday. It had name with the subtitle - day care and after school. Am I having competition even before my own afterschool program fully takes off?

The banner got me thinking (again!) -

The general understanding seems to be that 'day care' is for children under 5 years of age (snacks, play) and afterschool is for older children (snacks, homework, music, dance, art, puzzles, etc.). The latter usually does not offer a structured learning experience - it is loose collection of hobby classes, play time, etc., that the child opts in and out of. Both these are intended to care for the child - every day - till the parent picks her up after work.

The other kind of afterschool programs are not focussed on providing alternative child care. They are primarily learning centres giving the child what she/he would not get in school - a new way of learning (independent, exploration), a new level of learning (going beyond the curriculum), and new resources to learn from (not just prescribed textbooks). These try to squeeze themselves into the child's packed schedule - homework, tution, etc. - and are generally limited to once or twice a week. Abacus classes, Robotics clubs, etc. fit in better here.

Should both these different programs be then referred to as afterschool?