REALLY? That's a fascinating claim. How did you arrive at that; because you say so?
Let's look up what the two words mean because words apparently have no meaning to you.
es·tab·lish·ment [ih-stab-lish-muhnt] noun
1. the act or an instance of establishing.
2. the state or fact of being established.
3. something established; a constituted order or system.
4. ( often initial capital letter ) the existing power structure in society; the dominant groups in society and their customs or institutions; institutional authority (usually preceded by the ): The Establishment believes exploring outer space is worth any tax money spent.
5. ( often initial capital letter ) the dominant group in a field of endeavor, organization, etc. (usually preceded by the ): the literary Establishment.
sep·a·ra·tion [sep-uh-rey-shuhn] noun
1. an act or instance of separating or the state of being separated.
2. a place, line, or point of parting.
3. a gap, hole, rent, or the like.
4. something that separates or divides.
5. Law.
a. cessation of conjugal cohabitation, as by mutual consent.
b. judicial separation.
Sorry dunce; the only similarity is that they are both nouns.