From the perspective of the traveler the difference is somewhat semantics.
From the perspective of the US government, introducing the ESTA would have been much simpler than re-writing the various legislation around the Visa Waiver Program, which is likely why they went with this path.
However there is one major difference between the ESTA and an e-visa, and that is that with an ESTA, you don't have a visa. Where with an e-visa, you would.
Now that might seem obvious (because, well, it is!) but it's an important fact if only for one major reason - US Visa holders have more rights than people attempting to enter under the Visa Waiver Program.
If you hold a US visa, and you are denied entry at the border, then under US law you have the right to have your case heard by an immigration judge. If you are denied entry under the Visa Waiver Program - even if you hold a valid ESTA - then you have no such right.
The other difference between the two, which is the reason that people normally make the "ESTA isn't a visa" distinction around here, is that if you are "denied" an ESTA, then you have NOT been denied a US visa. This is important, as one of the questions asked when applying for a visa is whether you've been denied a visa previously. If the US instead used e-visas rather than ESTA, the answer to this question would be "yes" if you had been denied an e-visa, rather than no as it is today.