Milan Dinić

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Image descriptions are stored as content (field <code>post_content</code>) while captions are stored as excerpt (field <code>post_excerpt</code>). This means that descriptions are shown on single attachment pages, while captions are shown in <a href="https://codex.wordpress.org/Gallery_Shortcode" rel="nofollow ugc">galleries</a> and if image is embedded in a post content with a <code>[caption]</code> shortcode.
If you use images just in galleries, in order to have text below image in both places, you need to fill both fields.
This plugin changes that. You only fill description field and that text is used as caption of image in galleries.
There are no options or settings, just enable plugin and everything works automatically.

Descriptions as Captions in Galleries

Show image descriptions as captions in galleries.

hornament

Plugin accesses the caption shortcode via <code>add_filter( \'img_caption_shortcode\', ... )</code>.
By default, image authors are read out of the description of the respective image. Therefore, they have to be tagged in a specific way: 
In the description of the respective image, accessible under ‘Media’ > ‘Edit’ > ‘Description’, the image author (or multiple image authors) have to be wrapped in <code><author></author></code> tags.
If there are no authors in image description, the plugin tries to read authors from the image’s Exif information. If successful, image authors are automatically saved into image description.

fla_Image Caption

Plugin to insert image authors automatically.

Descriptions as Captions in Galleries vs fla_Image Caption