Suppose person A commits a serious crime, is convicted, and is pardoned for it. Does A still have a criminal record? For instance, I understand that a criminal record in the US means that you cannot vote in some elections. Equally, a criminal record can prevent entry to certain countries.
Pardons at the state and federal level have the effect of erasing the conviction. A disenfranchised felon who receives a pardon may vote again, for example. This is the main reason why people who have served their time and become upstanding citizens may still seek pardons: it may restore some rights which they never got back after leaving the pokey.
Some states also have a separate concept of “expungement” which is not exactly the same as a pardon, but I never really did get the difference.
In jurisdictions where the “royal” applies, a pardon excuses the person pardoned from the consequences of a conviction (ie, the sentence), but not from the conviction itself. See R v Foster [1985] 1 QB 115; R v Home Secretary; Ex parte Bentley [1994] QB 349.
In the earlier case, a person had the benefit of a pardon already, and sought in addition an order quashing the conviction, which was granted for the reason mentioned above - a quashing order would not have been necessary if a pardon already had that effect.
In the latter case, it was accepted that a pardon is not an acquittal, but recognised that pardons are only in practice given in cases where it can be established that the person convicted is morally and technically innocent.
The practice of giving out pardons at the end of a period of incumbency (as seems to occur in the US tradition) does not generally apply in Commonwealth countries where practices are derived from the notion of Crown privileges.