ESI is the same as what the old XML API was. An API, to get data about the game. So yes, they are the same thing in that regard, but ESI uses a diff method of authorization. The XML API used an api Key and vCode. While esi uses a token system using OAuth2.
The old API also worked in that you could get the same result using diff methods, as both ESI and the XML API boil down to making HTTP requests.
Postman is just an HTTP client used to make HTTP requests.
cURL is a command line based utility for data transfer, including HTTP requests.
Endpoint meaning what route of ESI you are requesting. You can see each route in the UI by clicking on a category. For example
Each of those would be a different endpoint under the universe category. Each row tells you what type of HTTP request it is, the route itself, and what it does.