Change Shopping Cart Title

You can change this directly in the checkout i18l file:

app/code/Magento/Checkout/i18n/en_US.csv

in your theme, like:

app/design/frontend/Vendor/theme/i18n/en_US.csv

Just change string translation like this:

"Shopping Cart","Basket"

Result:

Or you can create a language pack https://devdocs.magento.com/guides/v2.3/config-guide/cli/config-cli-subcommands-i18n.html

To translate a minicart title you must run setup:static-content:deploy with required parameters (More Info in DevDocs). After that translations must present in the js-translation.json file (pub/static/frontend/Vendor/theme/en_US/js-translation.json):

and result will be visible on the frontend:

The best and easiest solution that I found and that will not affect the default MAGENTO 2 structure (just changed under my theme) is by Prashant Valanda on "How to modify page title?" article.

Basically you just need to add this code in your XML file. In this case checkout_cart_index.xml:

<referenceBlock name="page.main.title">
    <action method="setPageTitle">
        <argument translate="true" name="title" xsi:type="string">Basket</argument>
    </action>
</referenceBlock>

After change doesn't forget to flush the cache.

php bin/magento cache:flush