Prokaryotic transcription involves RNA polymerase binding to promoter sequences on DNA and synthesizing RNA without the need for primers. It proceeds through initiation, elongation, and termination stages. Eukaryotic transcription is more complex, utilizing three RNA polymerases and involving transcription factors, mediator complexes, 5' capping, splicing, and 3' polyadenylation to process mRNA. Alternative splicing allows single genes to code for multiple proteins through different combinations of exons.