Magento 2: How to Change shipping message?

You need to override shipping.html in your theme from vendor/magento/module-checkout/view/frontend/web/template/shipping.html.

With Custom Theme:

Copy vendor shipping.html file to your custom theme at app/design/frontend/Vendor/theme/Magento_Checkout/web/template/shipping.html

Note: Make sure you first delete static shipping.html from pub/static from pub/static/frontend/Vendor/theme/en_US/Magento_Checkout/template/shipping.html

Now change text at last no-quotes-block div to your custom message

<div class="no-quotes-block"><!-- ko i18n: 'Default Shipping Message Changed......'--><!-- /ko --></div>

Now flush cache and try.

OR With Custom Module:

Copy vendor shipping.html file to your custom module at app/code/Vendor/Module/view/frontend/web/template/shipping.html

Now add requirejs-config.js at app/code/Vendor/Theme/view/frontend/requirejs-config.js

var config = {
    map: {
        '*': {
            'Magento_Checkout/template/shipping.html': 
                'Vendor_Module/template/shipping.html'
        }
    }
};

Note: Make sure you first delete static shipping.html from pub/static from pub/static/frontend/vendor/module/en_US/Magento_Checkout/template/shipping.html

Now flush cache and try.

OUTPUT:

As far as I can see this sentence appears in two places:

vendor/magento/module-checkout/view/frontend/web/template/shipping.html

and

vendor/magento/module-checkout/view/frontend/web/template/cart/shipping-rates.html

Said that and depending on what you want to achieve you could:

Overwrite those files in your theme

By placing your own content in

app/design/frontend/{vendor}/{theme}/Magento_Checkout/web/template/cart/shipping.html

and

app/design/frontend/{vendor}/{theme}/Magento_Checkout/web/template/cart/shipping-rates.html

Overwrite those files in your extension

Create a requirejs-config.js in your extension

app/code/Namespace/Mudule/view/frontend/requirejs-config.js

and place the following content

    var config = {
    map: {
        '*': {
          'Magento_Checkout/template/cart/shipping-rates.html': 
              'Namespace_Module/template/cart/shipping-rates.html'
        }
  }
};