Magento – How to save backend form data in database in magento 2

I don't have a full explanation, but I have an idea.
All elements rendered with mage-init will/should be handled by some javascript code.
You are linking these buttons to a form, and the form is handled by this js file lib/web/mage/backend/form.js where a jquery ui widget is created.

These are the options for the widget

options: {
    handlersData: {
        save: {},
        saveAndContinueEdit: {
            action: {
                args: {
                    back: 'edit'
                }
            }
        },
        preview: {
            target: '_blank'
        }
    }
},

you can see a saveAndContinueEdit in there somewhere inside handlersData.
Looking for the usages of handlersData you end up in _beforeSubmit where some magic happens (I don't really understand everything in there), and at one point _processData is called.
Moving to _processData you will see something like this

if (attrName === 'action') {
    data[attrName] = this._getActionUrl(attrValue);
}

this means that the action of the form is changed based on the button pressed.

the _getActionUrl function looks like this

_getActionUrl: function(data) {
    if ($.type(data) === 'object') {
        return this._buildURL(this.oldAttributes.action, data.args);
    } else {
        return $.type(data) === 'string' ? data : this.oldAttributes.action;
    }
},

you can see in there data.args involved. The same variable in the widget options for saveAndContinueEdit.

Conclusion: When you set the role saveAndContinueEdit toa submit button, the action of the form is changed via js and back/edit is added to the url.

on_click is transformed to the onclick event and simply called.
I honestly have no idea why there are 2 ways of doing this. Maybe the delete actions didn't get refactored yet.

if ($flag === true) {
    $fieldset->addField(
    'logo_image', 'label', [
    'name' => 'logo_image',
    'label' => __('Logo Image'),
    'title' => __('Logo Image'),
    'renderer'  => '[Vendor]\[Module Name]\Block\Adminhtml\Quotation\Renderer\LogoImage',
        ]
    );

}

In LogoImage.php

<?php
namespace [Vendor]\[Module Name]\Block\Adminhtml\Quotation\Renderer;

use Magento\Backend\Block\Widget\Grid\Column\Renderer\AbstractRenderer;
use Magento\Framework\Object;
use Magento\Store\Model\StoreManagerInterface;

class LogoImage extends AbstractRenderer
{
   private $_storeManager;
   /**
    * @param \Magento\Backend\Block\Context $context
    * @param array $data
    */
   public function __construct(\Magento\Backend\Block\Context $context, 
StoreManagerInterface $storemanager, array $data = [])
   {
       $this->_storeManager = $storemanager;
       parent::__construct($context, $data);
       $this->_authorization = $context->getAuthorization();
   }
   /**
    * Renders grid column
    *
    * @param Object $row
    * @return  string
    */
   public function render(Object $row)
   {
       $mediaDirectory = $this->_storeManager->getStore()->getBaseUrl(
            \Magento\Framework\UrlInterface::URL_TYPE_MEDIA
    );
       $imageUrl = $mediaDirectory.'cart2quote/images/'.$this->_getValue($row);
       return '<img src="'.$imageUrl.'" width="50"/>';
   }
}