​The data-mage-init HTML attribute is used to initialize the jQuery UI widget for a specific HTML tag.

This attribute specifies the name of the widget and its configuration options as a JSON object.

The x-magento-init HTML attribute is used to initialize RequireJS modules for a specific HTML tag.

The data-ui HTML attribute does not exist in Adobe Commerce.

Verified Reference: [Adobe Commerce Developer Guide - Initialize JavaScript components using the

data-mage-init attribute]

To initialize the jQuery UI widget in Adobe Commerce, the data-mage-init attribute is used in the

HTML tag. This attribute allows specifying the widget's component and its configuration in a JSON

format. The x-magento-init is used for initializing JavaScript components in a similar manner but is

typically used within <script> tags. There's no standard data-ui attribute used for this purpose in

Magento 2.