Mosfets versus Transistors

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I just found out that mosfets are also transistors(metal oxide semiconductor field effect transistors). So to transfer digital signals you should use this kind of transistor. Are mosfets connected the same way like normal transistors? Why should you use mosfets only in push-pull circuits, what are parasitical capacities in this context?

Can you show me an emitter follower circuit using a mosfet?