No, they are different. Indeterminate means that it can "take on" multiple values. For example $\frac{0}{0}$ could be any number, or "infinity". It cannot be determined.
I think a more rigorous way to show that $\frac{0}{0}$ is indeterminate is by understanding that:
$$\lim_{x \to 0} \frac{x^2}{x} \
eq \lim_{x \to 0} \frac{x}{x}$$