All themes include a "Cart" feature that provides your visitors with visual feedback that they have added an item to purchase. It also provides them with the ability to adjust quantities or remove specific line items before they transition to Shopify's "Checkout" where they will provide customer information, shipping details and payment information.
Because the "Cart" is a part of your theme, those settings can be customized through the theme editor under Theme settings > Cart. The code for the "Cart" Drawer and Page styles are also available to modify if you were to work with a Shopify Expert.
Once your visitor selects "Checkout" they have transitioned from the "Cart" to "Checkout" which is no longer part of your theme and is controlled by Shopify.
In the Checkout, Shopify does allow for some basic style, color and image adjustments that are universal across all themes. To edit these options, select Checkout and customer accounts from the top dropdown in the theme editor, or refer to Shopify's guide on customizing the style of your checkout here.