A long wire is a wire at least about a wavelength long, usually fed at one end. A random wire is a wire of any convenient length, with a tuner or matching box making up the difference. Both are the cheapest antennas to build, and both ask more of the station than they seem to.
Long wires: lobes, not a beam
Plane containing the wire; the full pattern spins around it like a cone-shaped lobe. Longer wire: lobes crowd toward the wire axis.
As an unterminated wire grows longer in wavelengths, extra lobes appear and the main lobes swing toward the wire's own axis. Gain over a dipole grows slowly, and the pattern has many lobes and nulls, so a long wire is not a precise beam. Adding a terminating resistor at the far end turns a bidirectional pattern into a unidirectional one; this is how a rhombic or Beverage works.
Random wires: any length, but not any impedance
Schematic, ideal wire. Shaded: within 0.05 λ of a half-wave multiple. High impedance means high voltage and a hard job for the tuner.
Length on this band0.51 λ
Feed point impedancevery high: avoid
Any wire can be tuned, but the feed-point impedance depends on its length in wavelengths. The curve is a schematic from an ideal wire: it repeats every half wavelength and is very high near each multiple of a half wave. A tuner can match it, but high impedance means high voltage, and loss in the tuner and any feed line rises. Pick a length that avoids half-wave multiples on the bands you use; no one length is good on every band.
The station is part of it
No coax shield to keep the RF outside: the radio, its cables and your hands become part of the antenna system.
With the wire connected straight to the radio there is no coax shield to keep RF contained, so station equipment may carry significant RF current. You see it as a tingling mic, a hot case or a computer that glitches when you transmit. Keep this in check by:
Supplying a counterpoise: one or more wires, or a ground connection, at the feed point, rather than letting your cables act as one.
Putting the tuner at the wire's feed point, or using a transformer there (often 9:1) and running coax from it, with a common-mode choke.
Remembering that a tuner makes the radio happy but does not reduce losses in the wire's system; see Antenna tuners.