What is the difference between a response element and a enhancer?
Enhancers specifically bind transcription factors in an effort to obtain robust rates of transcription, in a very general fashion and may be upstream or downstream of a promoter. Remember that you don't need to receive a signal to produce housekeeping genes, regulated by general transcription factors, because they're always needed (in part). A response element can enhance or repress transcription depending on the stimulus. 

Vitamin D response element (VDRE) is a fair example: In response to your extracellular calcitriol or 1,25(OH)2D, the vitamin D receptor will complex with a number of proteins that bind at the VDRE, controlling transcription of various vitamin D-controlled gene targets.


  Vitamin D activity is mediated through binding of 1,25(OH)2D3 to the vitamin D receptor (VDR), which can regulate transcription of other genes involved in cell regulation, growth, and immunity. VDR modulates the expression of genes by forming a heterodimer complex with retinoid-X-receptors (RXR).


Source: http://www.wikipathways.org/index.php/Pathway:WP1531

And just as well, other promoters such as that for pro-parathyroid hormone contain VDRE sequences that suppress it's transcription (ref).