I will try keep it short, the difference is considerable and big (it can be called another language even, since prima facie they are mutually unintellgible for the most part when speaking).
The difference arises because of the written register differing greatly from the vernacular in the way it does in Chinese quite specifically (because of its analytic phonosemantic structure).
The closest you might be able to start to comprehend on it personally is say if a time traveller from a more archaic form of Turkish, came to talk to you today. Or you might get an inkling talking to another Turkic language person (say uzbek) and see how much you understand etc...but how much becomes understandable later (easily) with learning older cognates that may have left Turkish or vice versa.
Cantonese preserves lot of Tang-dynasty era language features/cognates in notably its
vernacular....in multiple different ways (both sound change of the syllable and also completely different syllable sometimes).
This is exacerbated by it being analytical just like Mandarin (their grammar ends up being near identical for example). More on that at the bottom.
When they say the writing is all the same, that is the written register that is "Standard"....shared to very large degree with Mandarin.
But 20th century, the "classical" literary form also took a big change (i.e it dropped with end of Qing dynasty and needs to be studied now though it is taught in chinese schools to some degree so chinese do have basic level to access their earlier historical literature).
In essence that drop means even Cantonese is now evolving
written registers that turns out fairly gobbledegook to a mandarin fella (i.e written that mimics its vernacular much more and uses same sounds etc)....as no one really studies the full range of chinese characters to that level (and then make sense of it).
This actually is now taking on a political dimension increasingly as HK finds this (written cantonese "way") a silent protest way to shield from CCP overreach.
If you have time for it you can read a whatsapp soundbite i wrote to some friends who enquired on very much the same thing earlier:
View attachment 32276
@Deliorman @UkroTurk 🚬 @T-123456 @Joe Shearer @VCheng @Saithan @Kartal1 @MisterLike
@Indos @Anmdt @AlphaMike et al.
An earlier look in this subforum on agglutination (that Dravidian, Turkic, Japonic and Korean share along with Austronesian and others ) vis a vis fusional/synthetic and analytical, the larger pages they are found contain related context:
Her cocuk senin benim gibi degil,bazi insanlar kandirilabilir. Uyusturucu bagimlilarina bak,ne aylelerden cikiyor. Benim eskiden önce ülkücü sonra da şeriatçı İslamcı olduğumu bilmiyordur arkadaşlar:)
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