I often hear people use one word when they mean the other.

Problem:
These two nouns are not synonyms.

Explanation:
I often hear people say something like “I have a theory about …”, such as “about why Janey stays out late” or “about why Jim does not like his boss” or “about why women generally have more close friends than do men”.

The primary definition of the noun “theory” is a substantiated group of statements that explain a set of phenomena.

In contrast, the primary meaning of the noun “hypothesis” is a proposed, tentative explanation for an observation or phenomenon.

As noted at Wikipedia, “A scientific method consists of the collection of data through observation and experimentation, and the formulation and testing of hypotheses.”

So one starts with observations, then formulates hypotheses to explain those observations, and then tests those hypotheses. Once those hypotheses have been validated, one can create a theory.

I believe that the common English blunder of using the word “theory” where the word “hypothesis” is required is consistent with my “Devolution toward Simpler” linguistic hypothesis. (Note that I call this a hypothesis, not a theory!)

It is simpler to say or write the two-syllable, six-letter “theory” than it is to say or write the four-syllable, ten-letter “hypothesis”.

Solution:
Use “hypothesis” for a proposition to explain an observation. Use “theory” to refer to an analysis of a collection of facts and their relation to each other.