<p> is a prose paragraph. It does not contain each of the sentences that make up a paragraph, but the entire paragraph, up to a full stop and paragraph break. We do not distinguish sentences.
We also use
<p> to generate "paragraphs" in verse texts, when in our reference editions such separations are established (cf. Structure of an Epic Poem).
For different chapters or subchapters in prose works, or to mark choral parts (strophe, antistrophe, etc.) in dramatic works, we use divisions
<div>, cf. <div>.