Dedicated servers are supposed to be for high-demand bandwidth needs, but if that’s the case, then how come shared hosting like godaddy.com gives me 15,000GB of bandwidth and 1,500GB of storage every month for less than six dollars a month, while dedicated servers like theplanet.com charge me for only 750GB of bandwidth and 512MB of data storage?
That doesn’t make a single bit of sense.

You probably mean data storage about 500GB not 512MB, correct? There’s no hard drive with a size of 512MB.
Anyway, your experience is the byproduct of a dangerous marketing technique (gimmick) called overselling. The gimmick has hit the market hard and has caused irreparable damage already.
some shared and dedicated providers tend to oversell resources promising unlimited this and that. They believe that most users would not use more than 2% of the resources that they pay for. For example, they believe that if one signs up for a 15,000GB bandwidth plan, you would not use more than roughly 200GB of it.
But what if you use up the whole 15,000GB of bandwidth or the whole of 1,500GB of storage? It unfortunately means automatic suspension of your hosting account. Most over sellers have specific clauses in their terms of service / Acceptable Use Policy that restricts your use of those resources indirectly. For example, they will set a rule that says: your account can have no more than 1000 files at any time. A WordPress install has about 962! So you can see where this is going. The set of rules are ridiculous.
In addition, those over sellers are playing another dangerous game. Some don’t even have the whole 15,000GB of bandwidth available but only a small fraction of it. It’s like credit cards, you might have a limit of $5000 but it doesn’t mean it’s your cash. One day you will have to repay it with interest.
There are two camps right now. Those that oversell and those that do not. Most customers end up getting their hosting with over sellers. So you can see how this is hurting the good guys that only promise small resource ratios that benefit both the customer and the provider.
Most likely, if you end up using the whole 750GB of bandwidth and the whole 500GB hard drive, the provider will not suspend your account because there are no hidden rules in their terms of service. Also, keep in mind that with a shared account, you are limited in your usage of the CPU and RAM. Again, if you use more than 10% of the CPU or more than 10% of the RAM, you account will be suspended. So be sure to read the terms of service. This is a non-issue with dedicated servers because you are the owner and can do whatever you please with it.
But like you said, this whole thing did raise a flag for you as it should have! It doesn’t make sense.
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If you have a high demand (ajka very busy0 website that go for the dedicated server. if you don’t, the go for the economical site, but be aware it may lag from time to time. It is your money.
Bandwidth and storage are often unlimited or unmetered because they aren’t the limiting factor of modern hosting equipment.
A popular site really begins to run in to problems with CPU processing time. Dynamic sites – especially ones like forums with a lot of user input – take up a lot of processing resources. Some shared hosts throttle CPU time to allow domains to stay online, but this means slow downs.
So while a dedicated host generally offers fixed bandwidth and storage, its because you’re getting your own PC or a fraction of a partitioned PC. Ultimately, this means more processing time and a capacity for higher simultaneous traffic.
Of course, the shared hosts do provide a great deal these days, and most people starting out are better off spending the $5 or $10 a month on a shared plan! When those new sites get popular though, they might very well have to upgrade to a hosting plan with "lower" storage & bandwidth.