Some time ago Greece did not have a single National Insurance scheme, like NI in the UK, but well over 100 separate insurance schemes providing healthcare and pensions for different types of workers. IKA was the biggest one and the one that interfaced with NI in the UK for the purposes of reciprocal benefits such as healthcare.
All of us who are UK State Pensioners qualify for healthcare in Greece, paid for by the UK, under an EU wide reciprocal healthcare scheme. DWP issues us with an S1 form that we take to IKA and IKA issues us with an IKA healthcare book exactly like any other Greek citizen who has worked and paid into IKA. The book is then used to obtain medical services from any doctor or hospital that cooperates with IKA, not all do. More recently there has been a lot of amalgamation in the workers' insurance sector. The healthcare part of virtually all insurers were united under the term EOPYY. More recently still the pension part of virtually all insurance schemes have also been amalgamated so now there is largely a single healthcare and pension scheme called EFKA. Most of us continue to refer to it as IKA and the healthcare part of it is generally referred to as EOPYY.
Technically you shouldn't use a UK issued EHIC once you have moved permanently to Greece although many people do. Whether a UK issued EHIC, or an IKA healthcare book obtained through an S1 Form, will still have any validity after Brexit will depend on the final deal with the EU or with any bilateral deals if there isn't a common EU one.
I believe you can get a discount at the water park just outside Varipetro near Chania, the one Kamisiana referred to as local, if you are resident. That will not necessarily apply to other water parks as they are privately owned so it is up to the owner. You can also get in free at the one near Varipetro if you are over 65, or you could the last time I went, which is quite a few years ago now.
As Carol pointed out any benefits in Greece are few and far between and usually restricted to very low incomes. Unemployment benefit lasts for a maximum of 1 year I think and there is no safety net after that. You also lose your healthcare when you have been unemployed for a year. The general rule is "No pay - no play". Some would depend on being both resident and tax resident.