If I have an e-commerce business, would sales generated online from a different state be considered as making money in a different state?

It depends. In general, if you have annual online sales totaling less than $500,000 from a State, you are not considered to have "nexus" (business presence) in that State. Not all States have adopted this standard, so you may need to check at least those states where you have significant sales. Also, if you use an online sales platform (like Shopify), they may be able to help you determine if you need to claim income for any State other than where your online business in physically located. 

Of course, all income is reported for Federal Tax purposes, regardless of what state generated the income.

There is not one authority for this issue, but here are two articles from reliable sources:

• Developments in state income tax nexus for remote sellers (Journal of Accountancy, October 2022)
• What Tax Nexus Means for Your Small Business (Motley Fool, August 2022)