Paper is padded to protect otherwise loose sheets from getting dirty, creased, damaged or disorganized. Now and then I get asked to mail loose stacks of paper, but packaging it in a way that ensures arrival in good condition is actually pretty difficult, especially with thin, lightweight paper. It's much easier and safer to send a pad rather than loose sheets.
The main parts of a pad are the backing, the cover, the binding, and the paper itself. Some pads such as legal pads and scratch pads have no covers but most others do - it's important to protect the top sheet and corners especially if the paper is expensive. You wouldn't care about that as in a legal pad because those are either very casual (like walking into a meeting with a pad) or if not, will be carried in a folio.
Otherwise, the meaningful differences between pads are in the paper itself, and in this store, where all of the paper is of good to great quality, the differences are mainly driven by purpose....for example, letter-writing, note-taking, sketching, etc.
Correspondence Paper
Paper for letter writing has either no lines or lines widely spaced - usually 9-10mm. This spacing has a long tradition, as evidenced by letters from 100-150 years ago. Nowadays, as letter-writing is infrequent, narrower lines are more common, but in old times when many people (even your most macho man) wrote in fanciful Spencerian or copperplate script wide lines were the norm. Such wide lines allowed for bold ascenders, descenders, flourishes and freedom of expression in general.
If you find a modern paper with wide-spaced lines or no lines you can bet that it was meant to be used for a letter. Normally these lines are faint light blue or gray so that they don't distract the reader or the writer, but they have to be dense enough for the writer to be able to see them - a problem I find myself running into more as I get older. On the other hand, they can't be so wide and light that they show through fountain pen ink, since printing inks are oil-based and tend to repel fountain pen inks, which are water-based.
The most popular correspondence paper sizes are A5 and B5, whch are smaller than A4 (which is close to "letter" size) sheets. I prefer the smaller A5 because I write short notes and would rather run out of room before things to say. B5 is fine too, especially with 10mm lines, but I can't fill an A4 sheet without boring even myself to death, much less my intended recipient.
Some great correspondence pads with wide or no lines include Bank Paper, Quoi de Neuf, Pergola, Cream Writing, White Writing, Airmail paper, etc. Some of these have matching envelopes or come in letter sets.
Note Taking, Sketching, Doodling
Paper for note-taking usually has narrower line spacings - 6-8mm - or 5mm grids. Narrower lines mean you can cram more words on a sheet as opposed to the more leisurely, relaxed feeling of wide-lined correspondence paper.
Some people like to take notes in a notebook while others like pads from which they can tear out sheets and file or organize them in a ring binder or some other storage method. If you need to write about various topics in no particular order and feel strongly about collating the results at some point, a pad might work better than a notebook.
Some great pads for note-taking include the Life letter-size, Noble Note, Tomoe River and Maruzen 6000 (although I consider the Maruzen more of a fancy "pencil tablet").
Of course, everything I've said above is a matter of preference. In terms of correspondence, a personal letter received on narrow-lined paper in a barely-legible scrawl with doodles and crossed out mistakes beats any email in my opinion.