What is the difference between modern atomic theory and the Buddhist atomic theory? Buddhism also employs certain technical terms such as Anu,Paramanu,Cunna,Kapala and so on at same time we can take following terms as counter part of Buddhist terms in modern science,atom,nucleus,electron etc.
A difference between modern atomic theory & Buddhist atomic theory is their respective purposes.
Modern atomic theory culminated in atomic bombs used to kill thousands of people.
Where as the Buddhist atomic theory has the purpose of realizing 'not-self' (anatta) & bringing the peace & love of selflessness.
So far as I know, if people talk about "atoms" in Theravada doctrine, they're referring to Kalapas.
So, an explanation of "kalapas" is an explanation of "the difference between modern atomic theory and the Buddhist atomic theory" (especially since an explanation of 'modern atomic theory' is probably off-topic on this site).
So perhaps the answers to this topic, Meaning of 'kalapas', would answer your question.
In short, modern scientists analyze the external universe from quarks to quasars in pursuit of "the ultimate reality". On the contrary, we Buddhists analyze the matter in our sense experience as patavi, apo, thejo, wayo - Mahābhūta
to get rid of the dilution (avijja) caused by Vijñāna(~consciousness) projected on Mahābhūta. This is the intention of kayanupassana as described in the great Satipattana Sutta.
From Rohitassa Sutta:AN 4.45
"I tell you, friend, that it is not possible by traveling to know or see or reach a far end of the cosmos where one does not take birth, age, die, pass away, or reappear. But at the same time, I tell you that there is no making an end of suffering & stress without reaching the end of the cosmos. Yet it is just within this fathom-long body, with its perception & intellect, that I declare that there is the cosmos, the origination of the cosmos, the cessation of the cosmos, and the path of practice leading to the cessation of the cosmos."