With a virus, there are 2 separate things that happen at different speeds, and not at the same time:
- Live virus comes in contact with your body, and starts replicating, and your body is emitting copies of the live virus in exhalation etc. You are contagious and can spread it to other people at this point.
- The virus starts damaging the body badly enough to do harm, or to provoke an immune system response that itself makes you feel ill. You know you are sick at this point.
These things are separate, and can run on totally different timelines, or may not happen at all, depending on the virus and the person. When a person has the disease (#1) but does not feel the effects of illness (#2), that is called "asymptomatic". You can be asymptomatic temporarily, which is what happens to almost everyone with COVID-19. Or, what happened for Typhoid Mary, you can be at #1 forever without any #2, so you never know you have it! That is called being a "carrier".
On a well-behaved virus, the two will happen about the same time, so a person will feel ill and go into seclusion to protect themselves and others.
On a more dangerous virus, the time lag between #1 and #2 is quite long, and/or some people experience mild #2 effects which they mistake for normal stress/tiredness/side effects of a drug they take for something else. Then, you have a perfect storm for a disease that spreads widely, because you have a lot of unwitting "carriers", at least temporarily.