上床 equals to the phrase "go to bed". 睡觉 equals to "sleep". 上床睡觉 means "go to bed and sleep". Is it clear?

“上床”是动作（action），“睡觉”是目的（purpose），自然而然的就会说“上床睡觉”。类似的例子有，上厕所撒尿，去医院看病，去学校读书，下馆子吃饭，等等。

上床不一定是去睡觉，我们可以在床上玩，例如看书、听音乐。 上床睡觉就明确的告诉我们，上床之后我们得睡觉。中华文化博大精深，值得我们去探索。 Sex is not necessarily going to bed, we can play in the bed, such as reading books, listening to music. Go to bed and clearly tell us that we should go to bed after bed.Profound Chinese culture, it is worth for us to explore.

go to somewhere（上床） do something（睡觉）

we like saying somethings connected to make the purpose more clear,you must used to it,but often we would say somethings drectly, just like im gonna sleep=睡觉，without going to bed