How is the model of an atom like an atom and how is it different? Also, what are the limitations to an atom model and the limitations of any model?
There have been several different atomic models over time.
JJ Thompson suggested the "plum pudding" atomic model. He imagined the atomic structure to be similar to a positively charged plum pudding with negatively charged electrons that were stuck on the outside. Thus, his model was inaccurate to its large, dispersed positive charge. This is inaccurate compared to the dense, positive charge of today's model.
Rutherford-Bohr also created a model of the atom. He proposed that the nucleus contained a tiny, dense, positive core that housed most of the atom's mass. He called this the nucleus. He suggested that the electrons circled this core much like the planets orbit the sun. This model accredited electrostatic forces to keep the electrons in orbit, instead of the gravity that keeps the planets in orbit.
Schrodinger proposed the cloud model. This model also suggests that there is a solid core. However, it proposes that the electrons travel within a cloud-like region. Because the electrons are traveling so fast, it is impossible to know where they are at any given moment.
Scientific models never fully depict natural phenomena. They are usually overly-simplified explanations of such. This is great because models are used to help people understand abstract concepts. The trade off is that the concept is not fully described with one model. Models are not to replace the data generated by a controlled experiment. A model is only as good as the resource that was used to generate it.