I think the closing </p> tag became required under the HTML 5 spec (2008). Before it was optional, except when using XHTML.

p stands for paragraph. It's not a line break

The spec on <p>:

"The start tag is required. The end tag may be omitted if the <p> element is immediately followed by an <address>, <article>, <aside>, <blockquote>, <details>, <div>, <dl>, <fieldset>, <figcaption>, <figure>, <footer>, <form>, h1, h2, h3, h4, h5, h6, <header>, <hgroup>, <hr>, <main>, <menu>, <nav>, <ol>, <pre>, <search>, <section>, <table>, <ul> or another <p> element, or if there is no more content in the parent element and the parent element is not an <a>, <audio>, <del>, <ins>, <map>, <noscript> or <video> element, or an autonomous custom element." [0][1]

[0] https://developer.mozilla.org/en-US/docs/Web/HTML/Reference/...

[1] https://html.spec.whatwg.org/#the-p-element

Nonetheless, <p> is automatically closed by the occurrence of another block-level element, like another <p> tag or ones like <div> or any header. <li> and <tr> have similar rules. We close them because we're not savages and want to see container tags balanced in the editor, but the html5 spec doesn't strictly require it.

I always assumed all tags should be closed.

AIUI plenty of tags don't need to be closed. `<input>`, `<hr>`, `<img>` are the first three off the top of my head. Probably in XHTML you would've self-closed them.

Those are different from <p> as they are always self-closing immediately and thus cannot even be manually closed. <p> is only automatically closed if there is no </p> before the next block element.