Are they just actually the same? Especially as in the following examples:
I realize then whom I love.
I know then whom I love.
To know something describes a steady state. To realize something is to transition from a condition of ignorance into knowledge. If you put it into a timeline, when you realize something you change from not knowing to knowing:
To realize contains the additional connotation that your knowledge is gained by introspection, contemplation, or a change in self-awareness. If someone merely tells you something, you wouldn't say I realized X. You would say instead I learned X or something similar. When you realize something, you assert that you've come to that knowledge under your own power.
If you realize that you're in love, then you have just had a revelation about where your feelings lie. One of the definitions of realize is:
To know something is more long-term, perhaps after having realized it. The first definition for know is:
They sound similar, but in usage to realize something is more of an "aha!" moment, while knowing something can last far longer than that. It may take you a while to come to a realization, but you will not actively realize something for a long period of time.