Urgent assignments or tasks are often those that are based on dependancies. For instance legal approval for external stakeholder messaging. And hence, it should be prioritised over important tasks.
An important task may or may not be based on dependencies. Important tasks maybe also be subjective. (An important task maybe more important to the person who it impacts the most and maybe less important for others).
Urgent taks impact a larger group - a team or process and hence are higher in value to business when compared to important tasks.