This question mainly examines the judgment of compound propositions and the determination of sufficient and necessary conditions.

From "if $p$ and $q$ are true", we know both $p$ and $q$ are true, then we can conclude that "$p$ or $q$ is true".

From "$p$ or $q$ is true", we know that at least one of $p$ and $q$ is a true proposition, which means $p$ and $q$ being true is not guaranteed.

In summary, "if $p$ and $q$ are true" is a sufficient but not necessary condition for "$p$ or $q$ is true".

Therefore, the answer should be: $\boxed{\text{sufficient but not necessary}}$.