The method of ecommerce CRO is the same on every platform: measure, find the leak, research why, fix or test. What changes is what you are allowed to change, how fast the store loads and which tools can run a test. Here is what to know for the most common store platforms.
Shopify
Shopify stores are built from theme templates and apps. Most of the checkout is controlled by Shopify, and every app can add scripts that slow the storefront. Conversion work centers on the product template, the cart and the choice of apps. See Shopify CRO for the Shopify specifics. If you are still working out how to improve your Shopify store, start with the ten essentials every store needs.
WooCommerce
WooCommerce conversion rate optimization starts from more freedom and more risk. WooCommerce runs on WordPress, so you control every template, including the checkout. The cost is weight: each plugin can add scripts and database work, and the cart and checkout cannot be fully cached, so they are often the slowest pages on the store. Typical WooCommerce findings are slow product pages caused by plugins, checkout fields left at their defaults, and payment options that load late on a phone. The free WordPress theme detector shows which theme and plugins a store page loads.
Amazon
Amazon conversion rate optimization is a different job, because Amazon controls the page layout. The levers are the listing itself: title, images, bullet points, A+ content, price and reviews. Amazon reports a listing's conversion rate as Unit Session Percentage in Seller Central, and brand-registered sellers can A/B test listing content with Amazon's Manage Your Experiments tool. The checkout and trust signals are Amazon's, so the work is about answering the shopper's questions in the listing.
Platforms that give you full control of the templates behave like WooCommerce: more freedom, and more ways to slow the store down. The audit order does not change. Check tracking first, then the busiest leaking template, then the checkout.