What is the difference (besides price) between normal, platinum, and iridium spark plugs?
Copper conducts better and is generally used in higher-performance/modified engines. In dedicated race cars resistor-less copper plugs are used.
Iridium and platinum plugs are chosen for their longevity only. You shouldn't gap iridiums because of potential damage to the tips. For that reason and their inferior conductivity, they aren't used in modified engines. Keep in mind their price, as well.
Any claims of more power or fuel efficiency of one type over another are pretty much baseless unless you were using the wrong plugs to begin with. Stick with what your owner's manual calls for unless you have a reason to upgrade/modify. For example, if you have a turbocharged car but are running more boost you might gap your plugs a little smaller to accommodate. The claims by parts stores to upgrade to the Triple-Spark Ultimate Unobtainium plugs are just upsells.
The main difference is the material that the 'tip' of the spark plug is made of - normal ones are usually copper, whereas the other two have tips made out of platinum or iridium.
Platinum and iridium tips tend to last longer - copper tends to erode over time so the spark plugs wear out - plus they're slightly better conductors and can produce a spark under more adverse conditions (like under high cylinder pressures on turbocharged cars that run high boost).
On an unmodified car that specifies normal plugs, platinum or iridium plugs won't make much of a difference apart from cost; I'd stick with the manufacturer's recommendation and change the plugs as per schedule. On an engine that has been modified with higher compression or more boost, it might be worth springing for platinum or iridium plugs.
Of course, on a car where those plugs are specified (usually due to the extended service interval for the plugs) you'll have to use them anyway.
I have used all three types of spark plugs in my cars (all Suzukis) and found quite a difference between the Iridium/Platinum and the Copper ones which are much cheaper. The reason being that the iridium and platinum tips are more resistant to erosion due to the sparking. So overall they provide better performance over their lifetime, and don't degrade in performance that rapidly, than copper ones. Invariably, the platinum ones worked best in terms of price and fuel efficiency did improve marginally. The iridium ones were no better than the platinum ones in terms of performance but provided better durability (about 15% more life), but not that much so I can't really justify the price difference. Do try the platinum ones once, I think you'd be happy with them.
Back to O.E.M (original equipment manufactured). The four types of plugs are copper, platinum, double platinum, iridium. The type of ignition system should be your first variable to the question. Old ignition systems had one coil that provided spark to 8 plugs. They survived off the copper plugs, they would require to be replaced at the 2 yr interval, sometimes one year for excessive driving. Today they are called coil packs, some packs serve 2 plugs or 4 plugs depending on cylinder configuration. Newer ignition systems have 6 or 8 individual coils for each plug-some of these types require iridium tips. None the less, go with your O.E.M. Natural gas engines run better with copper even some manuals specify otherwise. It is wise to use anti-seize to prevent plugs from "welding" themselves to your cylinder head. Some engine blocks are aluminum some are iron, some are steel and when they are mixed with a different metal, they tend to add challenge for removal. I'm not even going to talk about Ford engines, they are known for blowing out their plugs while driving-what a nightmare. Extracting a broken plug without proper tools and potentially damaging the plug thread. Spend the 1.00 and buy a small pack of it.
On my 1980 Camaro with v-6 burning oil on one cylinder I replaced the standard plugs with single platinum at the time. Went from changing plugs every 6000 miles and the oil burner every 2000 miles to about 25000 miles and the oil burning cylinder every 6000. The plug would be totally caked before any idle degradation or miss. Made it into a street/strip car with an old school 396 of about 450 hp, ran 11.70s @ 115 mph. Switch to double platinum with no noticeable loss of performance, improved idle quality with large cam and slight rich carburetor. Improved consistency as the plug life is increased on the hot rod with no degradation over much longer period. Less changes and waiting for the copper plug to slow means much more chance you will run quicker times on those good weather days. Switched from single platinum to double on my 02 Mustang GT, no real reason, but it is hard to argue with a 13.37 @ 104 mph on a mostly stock GT. Oh yea, gears help.
The main difference between Spark Plug types with regard to their construction material is the time that they maintain their profile before eroding.There is a difference in resistance of different materials, but this is not enough to make a noticeable difference, as normal OEM plug leads are of the resistive type for modern vehicles (any running injection systems or elelectronic ignition systems. Its my opinion that you should use the plugs specified by the OEM, however there is a judgement call on price! If you have the dealer service your car go with the longer life rare metal plugs, if you change them yourself save money and use copper! Obviously always ensure the correct plug specification for length, sealing type (tapered or flat with washer) and electrode protrusion (heat range).