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Well, you have to look at the bases behind both models of the atom.
The Bohr model is based on the fact that electrons in atoms have been observed to be at certain energy levels, and Niels Bohr reflected that by having the electrons orbit certain exact distances away from the nucleus (a ball of neutrons and protons) in an orbit (kind of like planets around the sun). In this model, electrons are spheres orbiting a certain way all the time.
The electron cloud model reflects deeper quantum theory in that everything is based on probability. The nucleus is still pretty much a ball of neutrons and protons. The electron clouds are spaces in which you expect with a certain probability (say a 90% chance, for example) that the electrons are somewhere inside the cloud. There are no more distinct orbits, and there is no saying "I know where the electron is." These clouds are just where the wave equation of the electrons say they "should" be.
To sum up:
Both are based on developments in quantum mechanics, both involve a centrally located mass of protons and neutrons (nucleus)
Bohr: Electrons distinct and follow a definite orbit around nucleus
Cloud: No definite orbit for electrons around nucleus, only probability distributions of where electron is likely to be.
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