公网 is the usual internet we use, if u use adsl or modem to connect,
教育网 is cernet which is kind of very large intranet, only exist within universities in china, and only university students allow to use cernet.
coz china tele only give a very small b/w for cernet connection to pubic internet, so very hard to connect for some publich internet user. however, cernet user are not allowed to go outside china unless u either pay for that or use proxy or socks to do so.
