Do you mean 'Big Ben is the bell in it.' or 'Big Ben is the bell, innit?'?

Both. 

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If the name of the structure that contains the Great Clock of the House of Parliament is "Clock Tower" (or Victoria Tower renamed Elizabeth Tower in 2012), then why is it popularly referred to as "Big Ben?"
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Big Ben is alternately used referring the bell itself, the Great Clock, or the tower in which they're located.
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When Big Ben rings the number of times equal to the current hour, it's after 4 other (smaller) bells have all played their 20-tone sequence that precedes the first strike of Big Ben on each hour. The clock is maintained with the objective of having the first strike of the hour occur within one second of the hour, UTC (erstwhile Greenwich Mean Time or GMT). IOW bankers should be able to set their watches by the chime of this clock. Maintenance men can slow the pendulum of Big Ben one second per hour by adding a British coin to a particular stack of coins held in place on the pendulum, or, they can speed it up by removing one coin. On the prelude to each hour chime of Big Ben, the two highest pitched bells each play their notes 5 times, while the lowest plays its note just 4 times and the second lowest of the 4 plays its note 6 times.
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Listeners on the far side of London hearing the chime of Big Ben both by radio reception AND live through the air, can hear the 12 o'clock peals 13 times. The first peal is via the radio alone, followed by 11 peals of the radio in unison with the live sound through the air, and the 13th peal is only via the air (not on the radio). These people are located far enough away from the House of Parliament such that the time it takes for the sound of Big Ben to reach them equals the time interval that separates each peal of Big Ben, about 4.5 seconds. Therefore, they hear the second radio peal while they're hearing the first live peal, etc.
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Radio ... Live
1          
2  .  .  . 1
3          2
4          3
5          4
6          5
7          6
8          7
9          8
10         9
11        10
12  .  .  11
           12

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Here's one everybody can enjoy!

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TEA WITH MILK

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Given two 8-ounce glasses, one half full of milk, the other half full of tea; what do you end up with, after the following:

Take a teaspoon of milk out of the milk glass and stir it into the glass with tea in it.

Then take a teaspoon of the tea-milk mixture and stir it into the glass with the milk in it.

Is there more milk in the tea than tea in the milk, or more tea in the milk than milk in the tea?

There is more milk in the tea (1 teaspoon of milk was stirred into 4 ounces of tea) than tea in the milk (1 teaspoon of milk-tea mixture was stirred into the 4 ounces of milk. Thus only 1/2 teaspoon of tea + 1/2 teaspoon of milk was put into the 4 ounces of milk)

But one could also say that the 4 ounces of milk contains less tea (only 1/2 teaspoon of tea) and more milk.

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It went like this:
1 tsp milk removed from milk glass, added to tea glass = 
     tea glass = 100 parts tea + 1 part milk; milk glass = 100 parts milk - 1 part milk = 99 parts milk 
     Volume of tea glass = 101 parts            Volume of milk glass = 99 parts
1 tsp tea/milk mixture (99% tea, 1% milk) removed from tea glass, added to milk glass =
     tea glass = 99.0099... parts tea + 0.990099... part milk; milk glass = 99.0099... parts milk + 0.990099... part tea
     Simplified:  (99.01 parts tea + 0.99 part milk) in tea glass; (99.01 parts milk + 0.99 part tea) in milk glass
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Bottom Line - you end up with:
1 glass with 99% tea 1% milk, 1 glass with 1% tea 99% milk ---- IOW the same milk-in-tea, as tea-in-milk.
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The number of ounces in the glasses is irrelevant, so long as they are the same. (The original volume is 4 ounces each.)
They could be 20 oz or 3,419 ounce glasses, no difference. So long as they're the same volume.
The puzzle says, "8 ounce glasses... half full..." just to distract you and to make you think of half volumes. 
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The total volume in each glass, regardless of its size, is unchanged by the transfer. 
The same volume is removed, transferred, removed and transferred back.
So the first transfered volume is canceled by the second.
And the volume of milk transferred in the first teaspoon is exactly canceled with the volume of tea/milk transferred back.
If this process were repeated many times, eventually both glasses would end up with 50/50 tea and milk, with the same volume. 

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So far there are two puzzles in this thread nobody has tried to answer:
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What does how many tones in the Westminster Chime separate the midpoint of the only repetition of the same two pitches from the beginning of the repetition of the entire sequence of tones have in common with the variable pitches themselves?
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And another:
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If the Westminster Chime is rendered in the key of D, what pitch and octave does Big Ben have?