Minecraft: when is a modified client a hacked client?

Where is the limit / what makes the difference? Is there any commonly used definition?

If there are extensions inside that are used for cheating?

What if Minecraft's default code is changed? (But then Forge would also be a hacked client)

I would say if you installed mods with the intention of gaining an unfair gaming advantage it qualifies you to be called a hack client. But do not think that there's an exact definition.

Basically nothing speaks against "hack clients" or cheaty mods as long as they are not used on public multiplayers. In private with friends, I also use all kinds of mods that are simply forbidden on public servers.

Check the server rules of the server you want to play on or ask a supporter what is allowed on the server…

(this is always different you can be banned on Citybuild servers for 30 days if you use Badlion Client)

It's not about a server.

I'm programming a modified client. At first I copied a tutorial for a "hacked client". Every time I ask for help somewhere and say it is a hacked client, they refuse to help. Now I wanted to know if there's any / what exactly a "hacked client" is, as opposed to a normal modified client.

So if I program a function that does something automatically (e.g. Harvesting a field), it's a hacked client because it gives me an unfair advantage, right? Or in that case not because you could do it by hand?

Hard to say. You could also just pinch your mouse button. But if you program a nuker that harvests more than 1 field at a time, it is already cheating.

In principle, it depends on the amount of bad actions in which context you connect words. So the choice of words does it.

If you e.g. When you hear the word hack (in IT) you naturally think of criminal or at least questionable acts. Why? While you can hack into systems to test security and to find and close potential security gaps, you can just as easily break into systems with bad intentions to e.g. Deleting data without consent, stealing data, manipulating the system to distribute spam, etc.

The media prefer to report blatant stories that attract many readers, so messages like "50 million accounts from google, Facebook and Twitter are hacked!" Read more often than "Tom hacked into the coffee machine and changed the code so that the temperature sensor now measures a little more precisely". And so the word hacking is more likely to be associated with bad things and bad things only very few want to support.

So if you want to program a Fly mod everything is fine (unless you want to bypass the anticheat) but woe betide you want to program a Fly hack…

Servers therefore simply generally prohibit things that provide a significant advantage. This includes not only "hacks" such as fly, killaura etc. But also certain mods such as DamageIndicator, minimap with player display, ArrowCam, … GommeHD has listed all the things because they are constantly asked whether xy is allowed. Also macros etc. Prohibit many servers.