What are the common promoter elements found in eukaryotic genes, and how are they different from enhancer elements?

In eukaryotic cells you find core and proximal promoters.

Promotors are specific DNA sequences where transcription factors (proteins) and RNA polymerase binds to initiate transcription. Promotors are located upstream the coding sequence

Core promoters are where RNA polymersae binds and proximal promoters are where transcription factors bind.

Enhancer elements are DNA sequences where transcription factors (proteins) bind to increase the rate of expresion of an specific gene. Enhancers can be located either upstream,  downstream or thousands of nucleotids away  from the of the coding region.

Explanation:

Promoters and enhancer are key elements for controling gene regulation. Transcription begins when chromatin rearranges from a condensed state to a accesible state, this allow to transcrition factors and RNA polymerase to  bind specif DNA sequences (promotors).  Proteins bind to enhancers , this complex develops a DNA loop, so that the protein that is bound to the enhancer interacts with the RNA polymersase. When this interaction is made, the activity of the RNA polymerase is increased.