Are they made the same way as classical engines ?
Slightly simpler answer: the more volume of air/fuel you can burn (all around 13:1 air/fuel ratio) the more power you can produce. You can increase the static displacement (e.g. 3.7L V6 vs 2.5L four) or the engine speed. Formula One has always had restrictions on displacement, which required increasing the engine speed or increasing efficiency.
Formula One engines are always accelerating, which makes rotational inertia a concern. The less the better. However, reducing the mass also reduces the strength.
The limitations on engine speed come from friction which increases with engine speed and material strength. There have been street engines with relatively long strokes that could hit 9000 rpms: Honda S2000, Ferrari 458. Both had strokes over 3". However, in F1 the move to small bearings for reduced friction and less mass in connecting rods, crankshafts, piston pins, etc. for less inertia can make failure an issue. Metal valve springs are also subject to failure; racers frequently change them. F1 went to pneumatic valve springs a while ago. Valve stems can have strength issues. They are reduced in size for both less mass and less interference in the airflow.
F1 engines had gotten over 19000 rpms and were approaching 20k rpms years ago. F To reduce costs and increase competition the rules were changed to set an speed limit (19k in 2007, 18k in 2009) and limited the driver to 8 sealed engines for the season. There are also restrictions on bore size and materials used.
The result has been a dramatic increase in engine reliability, although there are failures because of the 8 engine rule.
Note: if rotational inertia wasn't a problem, it would be fairly simple to make an engine with components that could withstand the forces at 18k. However, when you want to minimize friction, minimize inertia, and maximize airflow the issues begin.
They are made quite differently than regular engines that we 'regular folks' have in our cars. Direct quote from http://en.wikipedia.org/wiki/Formula_One_engines :