One key distinction that stands out is the number of parameters accepted by each method - append takes two, while merge can take two or more.
Update:
Upon inspecting the code within these methods, another contrast emerges. The merge function will duplicate the properties from other objects whereas append simply copies them over.
Therefore, if one of the properties in an object or array is shared across multiple objects, modifying it through append will affect the original object as well:
var firstObj = {
name: 'John',
lastName: [ 'Doe' ]
};
var secondObj = {
age: '20',
sex: 'male',
lastName: [ 'Dorian' ]
};
//Object.merge(firstObj, secondObj);
Object.append(firstObj, secondObj);
console.log(firstObj.lastName[0]); // Dorian
secondObj.lastName[0] = 'McEnroe';
console.log(firstObj.lastName[0]); // McEnroe
Conversely, using merge preserves the independence between the array items in firstObj.lastName and secondObj.lastName. They remain distinct objects.
Fiddle: http://jsfiddle.net/Guffa/PrsXj/
Furthermore, the merge method offers a different functionality when the second parameter is a string:
merge(obj, "name", obj2)
This operation solely transfers the property obj2.name to obj, essentially equivalent to merge(obj, { name: obj2.name }).