No. You are confusing Hypertext Markup Language with Hypertext Visual Display Formatting.
The second example <p>...</p> says:
the content between the tags is a paragraph.
It does not say anything about what the text looks like, how wide or how tall it is, or how much space there is or isn't above or below.
It specifies the role of an element without attempting to dictate visual format. This is what mark-up languages do.