In my hc, all creatures of Equestria can create offspring with any other creature, with the offspring inheriting highly variable characteristics. The offspring of griffons and ponies follow these rules as well. while some hybrids may resemble one creature over another, an interesting convergence of traits results in some griffon/pony hybrids looking a lot like hippogriffs.
It's generally accepted in Equestria to call these guys "false hippogriffs." They typically are the direct offspring of a griffon parent and a pony parent, although they may rarely appear if the parent creatures have lineages involving griffons and ponies. They resemble true hippogriffs, with some exceptions: — ears more closely resemble pony ears, with increased fluff/feather cover — the placement of the false hippogriff's thumb digit more closely resembles a human's than a true hippogriff's — height is typically shorter, and weight is usually greater — false hippogriffs have no ability to transform like true ones — false hippogriffs are capable of earning cutie marks, although not every individual earns one — the flight ability of true hippogriffs is usually much more impressive than a false one's
Culturally, false hippogriffs overwhelmingly celebrate their hybrid heritage. Very few, however, seek community with true hippogriffs, and many will migrate to southern Equestria or Mt. Aris. Native hippogriffs are usually accepting of them, but some struggle to share their space with false hippogriffs. Due to ancient cultural rules, false hippogriffs are usually banned from participating in hippogriff rituals. This results in a general sense of alienation felt by migrant communities.
False hippogriff parents will almost always produce false hippogriff offspring. Once in a while, a variation of the griffon/pony hybrid may also appear, as well as offspring that are identical to pure griffons or ponies. Mt. Aris false hippogriff communities generally consider non-false hippogriff offspring a curse.