How is evolution both fact and theory?

In science, the first step in developing some idea or model of how the world works is to develop a "hypothesis". A hypothesis is usually based on the best evidence to date and still needs to be tested by other scientists. Other scientist try to "falsify" a hypothesis that is proposed and often try to float their own hypothesis. However, if a proposed hypothesis is not falsified, ie. no one can find a fatal flaw in it, it becomes a "theory". Theories are usually very well tested and essentially become the best explanation at the time of how the world works. This is different than common usage of the term "theory"

Scientists are often very reluctant to state that something is a "fact", as science is always open to new explanations that are more accurate. However, once theories make their way into university and high school textbooks they are pretty much "facts" or theories that have never been proven wrong.

Sometimes when very large theories are developed, like the The Big Bang, Evolution, or Plate tectonics they are called "paradigms".

So, Darwinian evolution at its core has never been "falsified", so it is both a "Theory", but also essentially, a biological fact. As one famous biologists stated...nothing in biology makes sense without evolution.