ESTA and visas are two different things:
- with ESTA, your country of origin is "trusted" and individuals in general undergo a lower level of scrutiny at a US port of entry.
- with a VISA, you country of origin is "not trusted" and individuals are granted the right to travel to the US after they undergo interviews at an US embassy and get approved.
Neither is a right to enter the US. Just a right to be transported by air/ship to a US port of entry. If the CBP lets you in it is a different story.
This is the US version. Other countries have their own rules.
And only one gives you a sticker on your passport
(And funnily enough the Visa lasts for a longer time)
Depends on the country. Eg. New Zealand and Australia don't put a visa sticker in your passport.