I'm reading about elliptic curves. Let $K$ denote a field $E$ denote an elliptic curve over $K$. From what I gather:
A principal divisor of $E$ is a divisor of the form $\mathrm{div}(f)$ for some $f \in \overline{K}(E)$.
A canonical divisor of $E$ is a divisor of the form $\mathrm{div}(\omega)$ for some non-zero differential $\omega \in \Omega_E$.
Every elliptic curve has an invariant differential $\omega$ with no zeroes or poles.
Hence $0$ is a canonical divisor of $E$.
The divisors of any two non-zero differential forms differ by a principal divisor.
Question. Does this mean that, on an elliptic curve, canonical and principal mean the same thing? If not, what have I misunderstood?