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They seem much like each other. What is their actual difference and what are their precise definitions?

My understanding of the two terms is much relied on the context of "Simple machines". The wikipedia articles of the two term provide a definition which makes them much similar but since simple machines are considered( of course by ancient greeks) as six distinct different basic machines they must have an important difference. I'm not sure but maybe modern treament of mechanical machines in terms of "Linkage synthesis" could give a better explanation. If it's possible please tell the differences and the definitions both in the context of "Simple machines" and "Linkage synthesis" methods.

A "Pulley" and a "Wheel and axle" seem much similar to each other. What is their actual difference and what are their precise definitions?

My understanding of the two terms is much relied on the context of Simple machines. The wikipedia articles of the two terms provide a definition which makes them seem very similar. But since simple machines are considered  (by ancient greeks) as six distinct different basic machines then they must have an important difference. 

I'm not sure, but maybe modern treament of mechanical machines in terms of "Linkage synthesis" could give a better explanation. If it's possible, please explain the differences and the definitions both in the context of "Simple machines" and "Linkage synthesis" methods.

They seem much like each other. What is their actual difference and what are their precise definitions?

EDIT(Question clarification):

My understanding of the two terms is much relied on the context of "Simple machines". The wikipedia articles of the two term provide a definition which makes them much similar but since simple machines are considered( of course by ancient greeks) as six distinct different basic machines they must have an important difference. I'm not sure but maybe modern treament of mechanical machines in terms of "Linkage synthesis" could give a better explanation. If it's possible please tell the differences and the definitions both in the context of "Simple machines" and "Linkage synthesis" methods. I hope I clarified my question well enough.

They seem much like each other. What is their actual difference and what are their precise definitions?

My understanding of the two terms is much relied on the context of "Simple machines". The wikipedia articles of the two term provide a definition which makes them much similar but since simple machines are considered( of course by ancient greeks) as six distinct different basic machines they must have an important difference. I'm not sure but maybe modern treament of mechanical machines in terms of "Linkage synthesis" could give a better explanation. If it's possible please tell the differences and the definitions both in the context of "Simple machines" and "Linkage synthesis" methods.

They seem much like each other. What is their actual difference and what are their precise definitions?

They seem much like each other. What is their actual difference and what are their precise definitions?

EDIT(Question clarification):

My understanding of the two terms is much relied on the context of "Simple machines". The wikipedia articles of the two term provide a definition which makes them much similar but since simple machines are considered( of course by ancient greeks) as six distinct different basic machines they must have an important difference. I'm not sure but maybe modern treament of mechanical machines in terms of "Linkage synthesis" could give a better explanation. If it's possible please tell the differences and the definitions both in the context of "Simple machines" and "Linkage synthesis" methods. I hope I clarified my question well enough.