what is the difference between the two theories of boltzmann and clausius stated on entropy?

One key difference is that Botlzmann's theory depends on the atomic theory of matter, whereas Clausius' definition and equation would work even if the atomic theory were false. Clausius' theory says nothing about WHY entropy tends to a maximum in all closed systems; it is blind to the fundamental mechanism(s). Whereas Boltzmann's theory not only quantifies entropy but asserts that entropy is directly proportional to the number of possible states of any sytem that result in the same temperature, pressure, etc.

Botlzmann's theory was ridiculed so harshly by sceptics of the atomic theory that he killed himself, according to some historians. And they may be correct. But as Hume said, a strictly empirical man who had lived in a hot desert his whole life would be justified in doubting reports of solid water (ice) until he had seen them for himself.