Answer:
All (electrical) coils are the same, in that they are coils. All coils honor the same principles: investing electrical energy into a coil results in a magnetic field. Investing magnetic energy into a coil results in an electric current.
But, different coils serve different purposes.
For example, a coil in an electromagnet is used to magnify the magnetic field surrounding a wire that carries an electric current. This is typically aided by supplying a core made from a a ferromagnetic material; that is, a material which offers very little resistance to magnetism. In an electromagnet, the coil and its core is typically stationary (even though the entire contraption might move, as is the case with a crane at the scrapyard). Therefore, the coil in an electromagnet converts electrical energy into magnetic energy.
The reversal of this process converts magnetic energy into electric energy, through a process known as induction. This is the case in dynamos, electric generators, and also in some electric motors.
Some machines make use only of the conversion from electric to magnetic energy, as is the case with the electro magnet. This group includes some forms of electric motors and generators.
Some machines make use only of the conversion from magnetic to electric energy, as is the case in the coil used to provide the ignition spark used with combustion engines.
Some machines make use of both effects. This includes transformers, and many forms of electric generators and motors. For example, a stationary coil in an electric motor might supply a magnetic field which acts on the rotor. If the field in the stationary magnet itself rotates, as is for example the case with 3-phase electric power systems, this rotating magnetic field induces an electric current in the rotor. The rotor could itself be a coil, which in response to this induced current creates a magnetic field, pulled around by the rotating field of the stationary part. (This is in fact the principle behind the most common electrical motor, the short-circuit motor)
Further uses of coils include that of (transient) energy storage: an electric current can build a magnetic field. When the current changes, the magnetic field also changes, and thus induces an electric current. This form of coils is frequently used in electronics to create filters; devices that suppress or select electric current according to its frequency. For example, your HiFi's loudspeakers contain a filter device that divides the electric signal from your amplifier into the higher frequency portions fit for your tweeter, and the lower frequency portions fit for your bass speaker.