A pandemic is an epidemic (rapidly spreading disease/virus) that's spread to multiple countries, meaning a pandemic can be caused by any infectious thing that spreads its shit. Plague is just sickness caused by a bacteria called yersinia pestis!

Edit: to add to the plague thing - we call pandemics plagues because of the fun times in medieval Europe when the plague caused a pandemic

Plague is not just referring to pestilence.

It can also refer to a pandemic of another disease, or also biblical swarms of locusts destroying the harvest.