The two phrases are NOT the same meaning although, as Gary says, their meanings are similar enough that one could easily misuse them. The "essence" of something is the most fundamental, central, essential part of it. It is the thing or things that, if taken away from something, that thing is no longer what it was. So... when you say, "In essence...." you are saying that you are getting rid of any extraneous, unimportant details and focusing on the core issues or features of the matter. The phrase "in fact" should be used to state something that you are asserting as factual and true to contrast against something that you are arguing is not true, incomplete or misleading. For example, one could say something like "Many people think of Arabs when they think of Islam. In fact, only 20% of Muslims are Arabs and over 60% of Muslims live in Asian countries."

They are similar, but there are slight differences. With 'in essence' - you would normally follow it with a statement that tries to clarify or simplify the situation. 'In fact' can be used the same way, but could also be a little more general, e.g. you could use it to add information, or change the topic slightly.