I think you are referring to a tooltip or popover which are inline poups to display text associated with the target text. MediaBox creates modal popups from a link to display some content from some other source such as an image, video or article.

Some Joomla templates might include the ability to display popover or tooltip text. Which template are you using?

I like to be able to activate a popup which explains with a text which gives an explanation for e.g. an abbreviation I use in my text. And ..... it should not be an URL

So you have some existing text on the site, on the same page as the text/abbreviation, and you want to display this in a modal popup?

Please try JCE MediaBox 2.2.4 Beta 2 - https://www.joomlacontenteditor.net/downloads/mediabox/development

Clear your browser cache after install.

You can now manually create a popup link that uses the contents of a local DOM element as the source of the popup, by specifying a data-mediabox-content attribute containing the element id as the value, eg:

<a data-mediabox-content="#contentId" data-mediabox="1" data-mediabox-width="480" data-mediabox-height="240">Click</a>

where contentId is the id of the element, eg:

<div id="contentId">This is some text to display in the popup</div>

To hide the element, use a nested structure, eg:

<div hidden>
    <div id="contentId">This is some text to display in the popup</div>
</div>