Still Unsure About Meaning Of Efficacy

It is great news that the Oxford/AstraZeneca vacinne has been given the nod although the pathetic jingoism emanating from the Government about British Science being the greatest is nauseating.
For some reason the Government is going ahead with the plan to give two full doses with 65% efficacy rather than the half followed by the full one which gave 90% efficacy which doesn't seem right, even if i understood what 65% efficacy meant.
To my mind, it means that for every 100 people exposed to Coronavirus, 35 will still fall ill but then the Oxford trial figures of 24,000 volunteers taking the inoculation and with 131 still catching Covid-19, even with my dodgy maths skills and inept use of a calculator, that despite receiving the vaccine, 0.5% - 0.6% of the 24,000 volunteers still fell ill, giving it an efficacy rating of 99.95%.
I also made the mistake of taking efficacy to mean the same as efficiency, saying the jab is 65% effective but that's also not right because efficacy means the rate in controlled laboratory conditions, effectiveness means out in the real world where other things may have an impact and the efficiency rate will only be known much further down the line after people have been injected. That told me.
So i am still not certain what efficacy means but its giving me a headache trying to work it out so i am going with two thirds will be fully protected with the remaining third not quite so fortunate and will still fall ill. I think.