The continuity is one of the best points in manga, comics of my own country are always episodic. I like the long and deep story's. I've got the feeling that most people like this part the most of manga together with the art.

Is episodic another term for a manga that have story arcs like One piece or Hunter x Hunter or is more extreme than that?

Unless it's a gag manga or something along those lines

Continuous manga are my favorite; it's nice to know a place and characters you've gotten to know so well will most like continue on for new adventures and bigger and better things. Episodic are good for when you're not in the mood for starting a new journey with characters you know nothing about, or not willing to dedicate yourself to another story you have to keep up with for fear of getting lost. It's so nice to be able to peek into an event in the lives of familiar characters and get all the pluses of a one-shot without nearly as much rushing to clarify personalities, intentions, and events.

Doesn't matter, but more 'none of the above' because some genres work better for one over the other, and it usually boils down to the writing quality. If a series is good in one of the options, it just is and you don't really notice. If it's bad, you notice the hell out of it.

Episodic
Pros: Cowboy Bebop, Desert Punk, Excel Saga, half of GitS, etc
Cons: ~85%+ of the longer running shoujo series

Continuous
Pros: Outlaw Star, Tower of God, Witch Hunter, other half of GitS, Baccano, etc
Cons: Naruto, Bleach, etc

Like some others say it depends on the genre, but also the style in which it's wirtten. I generally prefer romance and action manga to be continuous. Comedy can be episodic and some slice of life work great as episodic mangas as well.
I myself prefer continuous but it also depends on the plot and setting of the story.

"Depends on the series"

Aaaah, the eternal debate. This is a question that I have come around some times.

As other comments have said previously, it heavily depends on the genre. For a comedic mangas can hardly make a continuous plot, while action mangas do it better.

So basically each alternative has its pros and cons.

Episodic:
Pros: You can catch it or drop it anytime. You can read / see single episodes. It can provide a wider variety of situations.
Cons: It cannot address a longer or more complex scenes, since every single plot must be addressed in one chapter (just think in those 10 chapter fights in shonen). It doesn't get as addictive.

Continuous:
Pros: It can address arbitrarily long or complex plots or scenes. Its highly addictive and promotes fandom.
Cons: Its hard to catch up since you need to read every chapter in order. If you miss one chapter, you must recover it latter. You cannot read single chapters.

And thats my opinion. Me, personally I rather read continuous series since they are more addictive thanks to the cliffhangers at the end of the chapters. But some episodic mangas are also pretty good.