Praise be to Allah.
A number of scholars are of the view that pardon goes further than forgiveness, because ‘afw (pardon) means erasing and maghfirah (forgiveness) means concealing.
Abu Haamid al-Ghazaali (may Allah have mercy on him) said:
Al-‘Afuww (the Pardoner) is the One Who erases bad deeds and overlooks sins. This divine name is similar in meaning to al-Ghafoor (the Forgiving), but the meaning goes further, for forgiveness reflects the meaning of concealing, whereas pardon reflects the meaning of erasing, and erasing goes further than concealing. End quote from al-Maqsad al-Asna (p. 140).
Shaykh Muhammad Muneer ad-Dimashqi (may Allah have mercy on him) said in an-Nafahaat as-Salafiyyah (p. 87).
Pardon (‘afw) in the case of Allah, may He be exalted, refers to removing the traces of sin altogether, and erasing them from the record of the noble scribes [i.e., the angels], so Allah will not hold a person accountable for them on the Day of Resurrection; He will cause the sinners to forget them, so that they will not feel embarrassed when they remember them, and He will replace every bad deed with a good deed in the record. Pardon goes further than forgiveness, because forgiveness (maghfirah) reflects the meaning of concealment, whereas pardon (‘afw) reflects the meaning of erasing, and erasing goes further than concealing. End quote.
Other scholars were of the view that forgiveness goes further than pardon, because it is concealing and leads to waiving of the punishment and attaining reward. As for pardon, it does not imply concealing or attaining reward.
Ibn Jazziy (may Allah have mercy on him) said:
Pardon (‘afw) means not bringing a person to account for sin.
Forgiveness (maghfirah) means, in addition to that, concealing.
Mercy (rahmah) includes all of that, in addition to bestowing blessings. End quote from at-Tasheel (1/143).
Ar-Raazi said in his Tafseer (7/124):
Pardon means waiving the punishment from a person, and forgiveness means concealing his misdemeanour, to protect him from the pain of embarrassment and scandal, such as when a person says: I ask You for pardon, and if You pardon me, then please conceal my misdemeanour. End quote.
Al-Kafawi (may Allah have mercy on him) said:
Forgiveness implies waiving of the punishment and attaining reward, and no one deserves that except a believer; this word is used only in relation to Allah, may He be exalted [for only He can forgive in this manner].
Pardon implies waiving of blame and condemnation, but it does not imply attaining reward. End quote from al-Kulliyyaat (p. 666).
Al-‘Askari said in al-Furooq (413-414):
The difference between pardon and forgiveness:
Forgiveness (maghfirah) implies the waiving of punishment, and the waiving of punishment implies that the reward is inevitable, so no one deserves forgiveness except the believer who is deserving of reward. Hence this word is only used in relation to Allah, so it is said: May Allah forgive you (Ghafar Allahu laka), and it is not said: May Zayd forgive you, except very rarely…
Pardon (‘afw) implies waiving of blame and condemnation, but it does not imply that reward is inevitable. Hence this word may be used in relation to people, so it may be said: Zayd pardoned (‘afa) ‘Amr; but if he pardons him, he does not have to reward him.
However, because these words are very close in meaning, they overlap, and when speaking of the attributes of Allah, may He be exalted, they may be used to refer to the same thing. So it may be said that Allah pardoned him (‘Afa Allahu ‘anhu) and He forgave him (Ghara lahu), meaning the same thing.
What comes after the two words supports what we say. If you say, He pardoned him, this implies removal of something from him; if you say, He forgave him, that implies affirming something for him. End quote.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
Pardon implies waiving His rights in their case and forgiving them. Forgiveness implies protecting them from the evil of their sin, turning to them [in mercy] and being pleased with them, in contrast to mere pardon, for the Pardoner may pardon, but He may not turn [in mercy] to the one whom He pardons and He may not be pleased with him.
Pardon is mere overlooking, whereas forgiveness is kindness, grace and generosity. End quote from Majmoo‘ al-Fataawa (14/140).
Thus it becomes clear that forgiveness goes further than pardon, according to the correct view, because of what it implies of kindness and generosity.
As for the view that forgiveness refers to Allah pardoning you for sin whilst leaving it in your record, and that forgiveness refers to overlooking it and also erasing it from your record, there is no evidence for that.
And Allah knows best.