Keep in mind in that picture, there's three types of nibs. I'll explain.
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First and probably most important, is the G-pen. The reason this nib is probably the most important is because it's the one generally used to draw characters.
Okay, so the main thing that varies between these different nibs is their thickness, and how easy it is to change that thickness. For a G-pen, it's generally pretty thick, and the thickness varies VERY easily. Only slightly changing the pressure on your wrist is enough to change the thickness a LOT. The nib makes no effort to have consistent thickness.
Because of this, it's great for lines with varying thickness -- once you learn to control the G-pen well, you can draw very lively lines. Here's an example:
This is a page from Naruto. Naruto is a manga drawn almost entirely by the G-pen, including a lot of the backgrounds (but not everything, of course,) which gives it a rougher more "lively" look, and the backgrounds look more fantastical and completely unrealistic. This isn't just because of the building's designs -- it is because of the way the buildings are drawn.
In this page, you can see the G-pen in effect very clearly in Naruto's hair, bottom left panel. See how the hair consistently varies in its thickness? That, there, is the G-pen. Controlling it is difficult, but once you can control it, it's very versatile and the lines it makes feel genuinely alive. (it's worth noting that this page actually also displays exquisitely
bad control of the g-pen and in general bad lineart, but whatever, it's the fastest thing I could find. it was probably lined mostly by an assistant.)
So the G-pen nib looks like
this and you can tell it's a G-pen because, hey, it has a G on it.
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Then you get the Kabura pen. It's also called other things, such as spoon, egg, tama, saji, and a bunch of other shit. Basically, it's shaped like a spoon, and it looks like
this . What's the Kabura pen's advantage? The spoon shape makes it the complete opposite of the G-pen, it makes an effort to stay the same thickness, and it's very easy to control. Long straight lines? Backgrounds? Kabura-pen. You get a thickness, and as long as your control isn't too poor, for the most part the line sticks to it.
The Kabura-pen results in very straight boring lines, but straight and boring is frequently necessary in manga, again, for things such as backgrounds. Using it for characters, however, would be boring and amateurish.
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Lastly, the maru-pen. That's the tiny one. Maru is a root that means something along the lines of circle or roudn, and the maru pen is unique in that it's completely closed off and round. (most of the nibs are shaped like crescents, whereas the maru nib is a whole circle.) It looks like
this.
Because of its unique shape and size, it generally requires a different penholder than the Kabura/G-Pen (though modern pen holders tend to be able to hold both.) In the picture the other user posted, the blue holder on the right is the one used for maru pens.
It's tiny and good for precise little lines, like details on buildings in backgrounds that require thinner lines than the Kabura-pen can realistically offer, as well as things such as details in the eyes, or strands of hair, etc. I'm sure you could come up with plenty of uses by thinking of your own art, and when you use precise thin lines. Maru-pens are probably the hardest to control, at least for me, the little guys rip the paper easily and in general are just hard to use.
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So, yeah, that's a bit of a summary. If you're interested in summaries of these things, you should probably read/watch Bakuman, because it goes over a lot of these things in simple detail.
By the way, manga paper does look precisely like that, but something you might be surprised by is that the grid lines are damn near invisible. They cant be scanned by a scanner, so once the page is scanned there's no grid lines. When looking at manga paper from far away, it just looks blank. You have to be looking at it in good lighting in order to see the grid. It allows the artist to set the page very well, and it still remains not invasive to the art for viewers/scanners/whatever. Pretty cool stuff. I mean, not really, it's just light blue lines... but y'know. still.
also, another very important thing is screentones, which are used to "color" manga. that is to say, anything that isnt pure black or pure white, is made by a screentone. they are the manga world's "grey." it's kind of hard to explain how they work, so just google it and watch a video or something.