Smallpox has a relatively long incubation period of 7 to 17 days. And you weren’t infectious until the fever started. This gives your immune system time to mobilize and squash the infection before you become infectious to other people. It still takes time for a vaccinated person to get their immune system geared up to fight. It’s just that if you’ve already been exposed to a pathogen it takes ~5 days.
The first time your immune system encounters a new pathogen it takes a little over two weeks. In that time the adaptive immune system creates new antibodies and starts manufacturing a bunch of them. If you’ve been vaccinated the antibodies are already developed and the body just has to churn out enough of them to control the infection. At least that’s one level of what’s going on.
COVID-19 you’re infectious in just a day or two of being exposed and often have infected another person before the ramp up period of your immune system is over.
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