I've seen pictures of the source sheets. They pack many different cards per plate, not one card repeated a hundread times in the same plate.
Suppose that a set contains 300 cards and there are 3 plates with 100 cards each. If there are 100 rares, 100 uncommons, and 100 commons, I'd imagine that there is one plate with rares only, one with uncommons only, the third with commons only. Is this how they distribute the cards' rarities?
Note that Wizards tends to be fairly secretive about the specifics of how their print runs work, and exactly what a print sheet looks like. We occasionally get articles like the one that Zags linked to showing an entire print sheet, but most of the information we 'know' about the print runs has to be inferred from answers Wizards employees give or mathematical analysis of print runs.
Currently for a regular large expansion a set has 269 cards broken down as follows
A sheet of cards is 11x11 (121 cards total) as far as we have been able to tell so far the sheets are split up as follows (Source)
For the 2 Common sheets they are printed in a 3:2 ratio so that every common has the same rarity. The one exception is the 1 extra Common which has a rarity of 5:6, so it is very slightly rarer that the other hundred commons. This 101st Common is generally an artifact or land depending on the set.
These sheets are then printed so that the rarities are preserved both within and between each rarity, so each of the Uncommon sheets will be printed the same number of times so each Uncommon has the same likelihood of getting opened in a pack, and each of those sheets will be printed 3 times for every Rare/Mythic sheet that is printed.
This ends up with a booster pack that has 1 Basic Land, 1 Rare or Mythic Rare (7/8 chance of Rare, 1/8 chance of Mythic Rare), 3 Uncommons, and 10 Commons (one of the Commons has a chance of being Foil, about 1/6 (Source))
Note that all this information is about current large expansions. Small expansions have ratios that work out similarly. Special releases like the Commander decks, and other preconstructed decks have their own print runs (as Zags shows in their answer) and these cards are in addition to any cards in a normal print run, so for example any Rares in the Magic 2015 Intro Packs are more common than normal Rares that aren't in Intro Packs. Also as Zags also noted older sets had different print sheets where one card might appear on it 4 times, another card 5 times, and a third card 11 times (these numbers are based on Arabian Nights) Wizards has not done sheets for normal expansions like this for a while though.
Check out this article on how magic cards are made:
From this, we can identify several things:
Magic cards are printed by a company called Carta Mundi.
It appears Magic cards are printed in sheets. The oversized cards (from the commander sets) appear to be printed on 7x7 sheets and regular sized cards are printed on 11x11 sheets (though the Commander set may have been 10x10 so it was one sheet per deck).
Not just are magic cards printed in a quantity distribution of 1:7:24:88 (mythic:rare:uncommon:common) for rarity, but they are also printed in different quantities by language (English being the most common).
From this, we can deduce that each printing sheet has only cards of one rarity and language (with extras like tokens and informational cards to fill in the extras) and that they print different quantities of each sheet according to the amount of each they want to exist. So, they print 88 times more of the "English common sheets" for a set than they do of the "English mythic sheets" (though there are probably multiple sheets of commons and only one sheet of mythic rares). They likely also have separate sheets for foil cards.
That said, this is all speculation based on what we can observe. You would have to find a better article or contact one of the companies involved to get a more accurate answer (though they are probably protective of some of the secrets in their production process).
For a historic perspective, magic used to do finer granularity of rarity by having cards repeated on a sheet. So, in Antiquities, they printed 3x as many "common sheets" as they did "uncommon sheets", but there were cards that showed up twice on the uncommon sheets (dubbed "U2" in rarity) which would be twice as available as the "U1" cards (cards that appeared once on the uncommon sheet) but still rarer than cards that "C1" cards (cards that showed up once on the common sheet). See http://en.wikipedia.org/wiki/Antiquities_%28Magic:_The_Gathering%29 and http://www.crystalkeep.com/magic/misc/rarity-info.php for more on the history.
Every large set from Mirage through Onslaught as well as the core sets in between had 110 cards of each rarity indicating that the example in your question may not be that far off. During this period of time, Magic probably was printed as a 10x11 sheet of each rarity with just different numbers of each sheet printed to create different rarity. It looks like they switched back to 11x11 sheets between 9th and 10th editions.
Also possibly relevant: Are cards of the same "rarity level" really equally rare in MTG? and http://www.starcitygames.com/php/news/print.php?Article=11040
