A PODIUM is something you STAND ON -- from Greek pódion, 'little foot' and Latin pēs, 'foot'. (Note 'podiatrist' = foot doctor, and 'pedestrian' = walker, etc.)

A small chest-high table a person reads from or stands at is a LECTERN -- from Latin legere, 'to read'. (Also the root of legislation, 'written law [to be read]'; legibile, 'able to be read', lecture, 'to read aloud', etc.)