What is the difference between .catch and .fail in jQuery?

So I think the major difference is what you get out of each.

A catch allows you to run a single function.

A fail allows you to run a number of functions.

Other than that I concur with your findings. They are very similar.

I added an example code to showcase how fail will run both functions, and the catch will only run the one.

 $.ajax({
            url: "abc"
        }).done(function (data) {

        }).fail(function () {
            alert("a");
        }, function () {
            alert("b");
        })
                .catch(function () {
                    alert("c");
                }, function () {
                    alert("d");
                });

If you run this you get 'a','b','c' and then 'd' doesn't run.

I hope this simple example showcases the difference.

catch and fail are slightly different, in that catch will return a new (resolved) promise, whereas fail will return the original promise.

// This will only output "fail"
$.Deferred()
  .reject(new Error("something went wrong"))
  .fail(function() {
    console.log("fail");
  })
  .then(function() {
    console.log("then after fail");
  })

// This will output "catch" and "then after catch"
$.Deferred()
  .reject(new Error("something went wrong"))
  .catch(function() {
    console.log("catch");
  })
  .then(function() {
    console.log("then after catch");
  })

Note that catch(fn) is an alias of then(null, fn).