The mRNA in the new SARS-CoV-2 vaccines is, say the manufacturers, being produced by cell-free in vitro transcription from the corresponding DNA templates, or as nucleoside-modified mRNA. The BioNTech/Pfizer and Moderna vaccines both use mRNA encapsulated within a lipid particle. Once inside human cells, this encodes the viral S protein antigen which migrates to the host cell surface. The immune system then treats this synthesised protein as foreign, producing antibodies and T-cells and eliciting NAbs, so defending the body from any subsequent exposure to the virus.7,8.9 
Instability is a significant factor for mRNA which will degrade very rapidly if not stored under the right conditions, or if any contaminant ribonucleases are present. The lipid particle helps protect against ribonucleases in the extracellular spaces. 
The Oxford/AstraZeneca vaccine is a modified viral vector vaccine, described as a “recombinant, replication-deficient chimpanzee adenovirus vector” encoding the S protein antigen into host cells. The MHRA authorisation notes: “This product contains genetically modified organisms (GMOs).”

The seven vaccine candidates secured for early use in the UK, subject to authorisation, are:3,9,10,11,12