Both COVID-19 and SARS are caused by coronaviruses. The virus that causes SARS is known as SARS-CoV, while the virus that causes COVID-19 is known as SARS-CoV-2. There are also other types of human coronaviruses.
SARS-CoV, the virus that caused SARS, which was first identified in 2003 MERS-CoV, the virus that caused Middle East respiratory syndrome (MERS), which was first identified in 2012 SARS-CoV-2, the virus that causes COVID-19, which was first identified in 2019
Scientists have been looking at vaccines for coronaviurses at least since 2003 and possibly even before then. To say that the vaccines has been "rushed through" is grossly misleading.
Those vaccines you mentioned were all developed 70 or so years ago. The calculator I had at school in the 90's was more power than the most powerful computer in the world at that time so I would expect the development time of any new tech (vaccines included) to be better in 2020 than in 1955.
Also, when you pool the world's resources including government pressure into a common goal, things tend to happen at a lot quicker rate than if a commercial entity was trying to develop and market the new pill.
