Question: what is the difference between y and f(x)?
Answer: Functions are different in a key way from equations: a function is an output. An equation is a relationship between variables. Yes, y=x+3 and f(x)= x+3 yield the same results, which is why we teachers always tell you to remember that 'y and f(x) are the same thing'. However f(x) isn't a variable, but an output.