Debit card vs atm card HELP!!!!?

i went into capitol one bank becasue my mom wants me to have a debit card and we read you could be any age to have a debit card and we went in and we asked for a debit card but they gave us a atm card with my moms name on it and said i could use it!!! whats the deal??? why dindt i get a debit card like we wanted?? please help!! im frusterated