When you have either the wrong harmonic balancer or the wrong flexplate (flywheel), you will have a "shake" or a "shutter" from about 1,800 RPM to about 3,000 RPM. It'll begin to smooth-out above that. Well, actually it doesn't really smooth out in reality, it just oscillates so fast, you don't notice it as much.
When an engine is out of balance, or you have something like 1 rod cap on backwards, it will usually cause a vibration. What I mean between a shake and a vibration is the speed or "frequency" of how it presents.
A shake or shutter is like an off balance washing machine on the spin cycle. It actually makes the entire engine "wobble", which you can feel through the whole vehicle. A vibration, such as an engine out of balance" is more like, well.... a vibrator.
Most machine shops (and rightfully so) don't balance rotating asemblies. Neither did any factory. No engine ever came "balanced" from the factory. They would take a typical crank, a typical rod and a typical piston, do a rough balance on them and set all of the machines to make all of the parts the same. They never took into account for rod changes, batch changes, piston upgrades, etc. In other words, it was very "vague" on the balance numbers.
Now, when a machine shop does a balance job, we take everything into consideration, including the weight of the oil that is on the parts, and balance that to within 1/4 gram. Factory engines weren't even close to that kind of accuracy, in fact, they were usually pretty far off... by "ounces", not by grams.
If you have a "shake" or a shutter, you probably have a mismatched balancer or flywheel. It could even be a bent crank or a bent crank snout causing that shutter. I have seen this on a few engines over my years and have bent a few crank and snouts on small block Fords in the early days of supercharging.
If you have a "vibration", then it is probably a component within the rotating assembly. Not all engnies use the same components. In other words, if you had one bad rod, a machine shop might replace that rod. Well... that replacement rod is most definately a different weight from the other 7, thus potentially causing a vibration.
The only time you REALLY need to balance an engine is when you use after market components, such as a crank, rods or pistons, or any combination of the 3. After market components do NOT have the same weights as factory components, so you can't just go throw a set of after market pistons in, or a new set of rods, or a new steel crank and run with it (them). You HAVE to balance the assembly or you're asking for a vibration problem which will eat-up bearings.
Some people get very anal about balancing and when it comes time to "freshen-up" their engine, they may keep everything but swap out the pistons for forged types. Well, those are much heavier pistons (if you use something like Sealed Power's compared to a stock cast piston), so there went the balance job right out the window. This also rings true if you bore your block and go with a .030" over piston. You now have pistns with .030" more material on them, so naturally they are now heavier than your last set, so in theory, your engine needs to be re-balanced. The reality of it is though, you don't really need to balance it all again. There ARE tolerance areas where being a little off here or there won't make an effect on how "smooth" teh engine runs. Again, ALL facory engines fall into this category, except for maybe the very rare, special performance engines that came in limited edition cars.
Hope that helped