Are loss functions only used to evaluate estimators?

Given the likelihood $$p(x;\theta)$$, we want to construct an estimator $$\hat\theta(X)$$ that takes in the observation $$x$$ and returns an estimate of $$\theta$$. There are many different ways to evaluate our estimator $$\hat\theta(X)$$. For example, the bias of $$\hat\theta(X)$$ is $$\mathbb{E}_{p(x)}[\hat\theta(X) - \theta]$$ and the mean squared-error (MSE) of $$\hat\theta(X)$$ is $$\mathbb{E}_{p(x)}[(\hat\theta(X) - \theta)^2]$$ Both the bias and the MSE are functions of $$\hat\theta$$ and $$\theta$$, and it seems at first glance that they are examples of loss functions, since loss functions are also functions of $$\hat\theta$$ and $$\theta$$.

More generally, in the context of statistics, does this mean that loss functions are only used to evaluate estimators?