tierrainnovation

Smart Category Ordering is a plugin that allows you to sort your post content (per category). You can apply your sorting to a single category, or have your settings follow a category tree, covering the parent and children categories.
When sorting by “Smart Title”, that option is there to the leading ‘a’, ‘an’ or ‘the’ from a post title when sorting. This is the only difference between “Smart Title” and “Title.”

Smart Category Ordering

Allows you to alphabetize categories by post title, by trimming leading text, by post date.

Risto Niinemets

Most commonly taxonomy sorting plugins will create a new interface to drag or order/sort your terms. This plugin uses the built-in view just to make things easier. Just grab the term and drag it to a new position. No more extra clicks – everything is saved after repositioning!

The Taxonomy Sort

I would advise against using this plugin. In the latest WordPress update, selected categories are no longer displayed on the posts page. Deactivating the plugin shows the selected categories once again. It's too bad, this was a useful tool.

Broken in WordPress 4.7

Allows you to easily change the order of different taxonomies/terms/categories.

Smart Category Ordering vs The Taxonomy Sort