Firstly, prototypes are just objects. In this case, yes:
jQuery.prototype === jQuery.fn
So saying jQuery.fn.map = function() {} is like saying jQuery.prototype.map = function() {}
When you instantiate a new jquery object with $(selector | dom node | ...) you are returning a jQuery object which automatically inherits all the prototype methods, including map, tweet, etc. Research Javascript's prototypal inheritence model and how object prototypes work in regard to new
$ is just a reference to jQuery which returns a specially modified new object. $ is a function which returns a new object reference. Here's a simplified example (but you really should research more about prototypal inheritence, it has been answered many times repeatedly):
var A = function() {
};
A.prototype.doThing = function() {
};
var newObj = new A();
newObj.doThing // this new object has this method because it's on A's prototype
so newObj.doThing is just like $(selector).tweet
Also feel free to read the source of jQuery and trace what happens when a new object is created. You can see near the top exactly what is happening under the comment // Define a local copy of jQuery


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