Short answer: A shop-vac is better than nothing, but barely adequate for dust collection on almost any stationary power tool. On the other hand, a dust collector would be inappropriate and wouldn't work very well for most handheld tools.
Long answer: read on...
The others mentioned that a Shop-Vac produces low-volume air flow with high static pressure, and a dust collector produces high-volume air flow with low static pressure. But what does any of this really mean in practical terms?
CFM vs. Static Pressure, defined
Air volume is measured in cubic feet per minute, or CFM--the volume of air that the device can move from its intake to its exhaust in one minute.
Static pressure is measured in inches of water (often referred to as inches water column, or inches WC), as in, how many inches the suction device can lift water up a pipe.
In simple terms, static pressure determines how much resistance ("static pressure loss") your dust collector can overcome in order to move a given volume of air through the hoses and pipes. When it comes to designing a dust collection system, the raw CFM figure is initially more important than the raw static pressure figure, though static pressure does come into play once you start designing your ductwork (more on this later).
Is that enough CFM and static pressure?
WOOD Magazine has a great article on calculating CFM and static pressure requirements for dust collection. Although the worksheets in the article may look intimidating at first glance, they aren't too difficult to fill out. The article includes some typical CFM requirements for various tools, some of which I've included or summarized below.
- Table saw, radial arm saw, miter saw, bandsaw: 350 CFM
- Belt, disc, or drum sander: 350-550 CFM (depending on size)
- Table-mounted router: 195 CFM
- Thickness planer, up to 13": 400 CFM
- Thickness planer, 14"-20": 785 CFM
Now let's look at some contenders for an entry-level dust collection system. As of this writing, a "6.5 peak horsepower" Shop-Vac® vacuum rated at 9.3A@120V produces 185 CFM of airflow and 64 inches of pressure. That's not even adequate for the least-demanding machine in the list, falling 10 CFM short for a router table. In practical terms, this means the vacuum won't be able to produce the recommended 4000 FPM (feet per minute) linear air velocity necessary to capture most of the dust particles produced by the tool. (Note that the 4000 FPM figure somewhat oversimplifies things but it is a good, convenient figure for making realistic estimates.)
By comparison, a 1hp Grizzly dust collector rated at 8A@110V produces 500 CFM and 2.76" of static pressure. As you can see from the CFM figures above, under ideal conditions this dust collector should be able to capture most of the dust from most tools except larger sanders and 14" or larger planers.
Remember, I said that was under ideal conditions. This is where static pressure comes into play. Every inch of pipe or hose, every turn, and every change in diameter produces resistance which your dust collector (or vacuum) must overcome. You can use one of the various static pressure calculators such as Bill Pentz's static pressure Excel spreadsheet to calculate the static pressure drop produced by your ductwork and hoses. For the Grizzly 1hp dust collector we looked at earlier, the total static pressure drop can be no more than 2.76". If you plug only 2 feet of 4" flex hose into the calculator, you'll see the static pressure drop is more than 3", so we already need to look at a more powerful dust collector.
Although this is the simplest way to size a dust collector, you don't suddenly go from 500 CFM to 0 CFM. The excessive static pressure loss simply reduces the airflow through the system. Some manufacturers or magazines provide the CFM curves at various static pressures, which is helpful in determining whether you can sacrifice a few CFM for a longer run of pipe or hose while maintaining the recommended 4000 FPM air velocity.
Other considerations
In addition to the fact that a Shop-Vac just isn't suitable for stationary power tools, one of the dust collector's greatest advantages over a Shop-Vac is that it has a larger hose and is less likely to clog from chips and shavings. Whereas a Shop-Vac typically has a maximum hose size of around 2-1/2 inches, a dust collector hose (or pipe) is typically 4 inches or larger and is less likely to clog.
Getting back to your questions, you asked whether a dust collector can (1) pick up or (2) filter things that a shop-vac can't. We've already answered the first question (yes, a dust collector can "pick up" more). HEPA-rated filters can remove 99.97% of particles down to 0.3 microns. You can buy these types of filters for both Shop-Vacs and dust collectors, so technically the answer to the second question is yes but it just depends on what type of filter you buy (and, in some cases, how determined you are to adapt such a filter to your machine if your manufacturer doesn't offer one).