The two suits of armour have always generally been assumed to be the same one. There are a few discrepancies but they can be explained by Boba customising it along with years of wear and tear.
In The Clone Wars episode "R2 Come Home", Boba rigs his father's helmet to explode in an attempt to kill Mace Windu. The canon-ish Star Wars: Absolutely Everything You Need to Know confirms that this is Jango's helmet, not a duplicate, so it may have been recovered, reforged, or replaced by the time of the original trilogy.
Absolutely Everything also says Boba "patches together" his own suit of armour, which might suggest he didn't have all the parts and had to improvise. If he had the helmet, he could reasonably have had the rest.
Overall, the story seems to be that Boba recovered his father's armour somehow and used it for himself, repairing and customising it as needed. The two armours look similar enough in Attack of the Clones and The Empire Strikes Back that I think that was always the intended interpretation.
How much he can replace and have it still be his father's armour is one for the philosophers.