What is the difference between a p element and a paragraph with text?

Question

I have read similar questions but still have some confusion and asked.

Premise

According to the HTML Standard, the p element represents a paragraph.

4.4.1 The p element

The p element represents a paragraph.

And the HTML Standard's explanation for paragraphs reads as follows:

A paragraph is typically a run of phrasing content that forms a block of text with one or more sentences that discuss a particular topic, as in typography, but can also be used for more general thematic grouping. For instance, an address is also a paragraph, as is a part of a form, a byline, or a stanza in a poem.

Here, according to NOTE, the p element is one of several that represent a paragraph. Also, the term paragraph as defined in this section is used for more than just the definition of the p element.

The term paragraph as defined in this section is used for more than just the definition of the p element. The paragraph concept defined here is used to describe how to interpret documents. The p element is merely one of several ways of marking up a paragraph.

Furthermore, the following HTML considers text to be a paragraph and states that there are five paragraphs.

<section>
 <h1>My Cats</h1>
 You can play with my cat simulator.
 <object data="cats.sim">
  To see the cat simulator, use one of the following links:
  <ul>
   <li><a href="cats.sim">Download simulator file</a>
   <li><a href="https://sims.example.com/watch?v=LYds5xY4INU">Use online simulator</a>
  </ul>
  Alternatively, upgrade to the Mellblom Browser.
 </object>
 I'm quite proud of it.
</section>

1. The paragraph that says "You can play with my cat simulator. object I'm quite proud of it.", where object is the object element.
2. The paragraph that says "To see the cat simulator, use one of the following links:".
3. The paragraph that says "Download simulator file".
4. The paragraph that says "Use online simulator".
5. The paragraph that says "Alternatively, upgrade to the Mellblom Browser.".

Question 1

The five paragraphs shown in the code contain text. Does this indicate that semantically text also represents a paragraph?

Question 2

The description of the p element says that the p element represents a paragraph. However, the paragraph section says "the p element is one of several that represent a paragraph" and "the term paragraph as defined in this section is used for more than just the definition of the p element.

In other words, the paragraph section does not clarify what kind of paragraph the p element represents. What is the exact definition of the p element?

Answer 1

question 1: yes

question 2: The p element creates a paragraph, the contiguous section of longer text. However, in HTML, p can be used for any type of contiguous content to be grouped, for example, images or form fields.

Answer 2

I would simply regard p elements as paragraphs of "plain text content", as opposed to headers, lists, quotes etc. for which there are separate tags in HTML.

Of course you can also create a paragraph using a div or span tags defining their styling with CSS (using classes or IDs) and thereby making them look like regular p paragraphs. Even the "non-paragraphs" in your example which are basically formed by being between two other tags without having a tag of their own as delimiters will look like p text if their parent container has CSS rules (or just default settings) that is equal or similar to p tags.

But semantically, only a p tag is "regular" text content (i.e. not having a function like being a header, part of a list, a blockquote or whatever HTML supplies tags for). If you think in terms of acessibility or SEO, this makes a difference, even if you don't see it.