Answer:
Westward expansion: the 19th-century movement of settlers into the American West, began with the Louisiana Purchase and was fueled by the Gold Rush, the Oregon Trail and a belief in "Manifest Destiny."
Western Frontier expansion: with European colonial settlements in the early 17th century and ended with the admission of the last few territories as states in 1912. This era of massive migration and settlement was particularly encouraged by President Thomas Jefferson following the Louisiana Purchase, giving rise to the expansionist attitude known as "Manifest Destiny"
So saying that I would guess that they are many names for the same thing. They also both refer to "Manifest Destiny".