This is highly dependent on the product you are working on, the technology stack used to build it, the team that built is, and how security has been handled so far. If you are asking because you want to start a security investigation, you will probably want to talk with your development team to organize that work.
I think Security testing is the main part that needs to be considered in ecommerce testing. Othet major types of software testing that must be implemented for effective omnichannel retailing and ecommerce website are ;
1. Functional testing
2. Mobile Testing
3. Compatibility testing
4. Load & Performance Testing
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