A polynomial has more than one term in it. y^3 is not a polynomial just as it is not a binomial, trinomial, etc.
Any numbers or variables separated by addition or subtraction are separate terms.
A binomial has 2 terms because the prefix bi- means 2. A trinomial has 3 terms because the prefix tri- means 3.
x + 5 is a polynomial and a binomial.
x^2 + 8x - 3 is a polynomial and a trinomial.
The previous answerer gave a good explanation. I'll just add to it a bit by saying y^3 is a
MONONOMIAL. Since it has 3 as an exponent, we say it is a mononomial of degree 3