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.

Marco Buttarini

Add IPTC credit to the caption of the image after have uploaded it.

Credit2Caption

Add IPTC credit to the caption of the image after have uploaded it.

Descriptions as Captions in Galleries vs Credit2Caption