ESL = English as Second Language
EAL = English as Additional Language
Those terms means the same things, however there is no real precise definition of what it means. For the assessment you are using, this is the definition we are using.
ESL/EAL means:
at home, your parents do not necessarily speak in English (father, mother or relatives)
at school, all the education sessions are in English, including Maths, Physics, Chemistry (science in the large) History, Geography, etc...
To summarize: English is the language of your education, not an education subject like History or French.