There's so much confusion around this subject, and none of the existing answers cover everything clearly and directly. Here are some examples with comments inline.
//this is a declaration
var foo;
//this is an assignment
bar = 3;
//this is a declaration and an assignment
var dual = 5;
A declaration sets a DontDelete flag. An assignment does not.
A declaration ties that variable to the current scope.
A variable assigned but not declared will look for a scope to attach itself to. That means it will traverse up the food-chain of scope until a variable with the same name is found. If none is found, it will be attached to the top-level scope (which is commonly referred to as global).
function example(){
//is a member of the scope defined by the function example
var foo;
//this function is also part of the scope of the function example
var bar = function(){
foo = 12; // traverses scope and assigns example.foo to 12
}
}
function something_different(){
foo = 15; // traverses scope and assigns global.foo to 15
}
For a very clear description of what is happening, this analysis of the delete function covers variable instantiation and assignment extensively.