Primer- single stranded piece of DNA with a complementary base sequence to the start of a gene/ section of DNA you want to copy (usually by PCR). Acts as an attachment site for a type of DNA Polymerase enzyme, they bind to a specific section of DNA that has been separated by heating and the enzyme can then bind and form new strands.
Promoter- A sequence of DNA that occurs before the gene that allows RNA polymerase and transcriptional factors to bind (so gene can be transcribed and then translated).