This question may have slightly different answers in different English-speaking countries, but in the US, the verdict is the decision itself. After hearing the evidence in the case, the judge or jury will deliberate and then "render the verdict," or "deliver the verdict." This will usually take the form of a pronouncement that the person is "guilty" or "not guilty." If you watch American TV or movies, you will see one of the jury members being asked to report its verdict in a formula that goes something like this:
"On the charge of murder, we the jury find the defendant not guilty."
The conviction is the fact of the person's being found guilty of the crime. For example,
"After his conviction for murder, the man was sentenced to 25 years in
prison."