Introduction: The half wave end fed antenna is simply a half wavelength wire fed at the end rather than the center like the half wave dipole. The impedance of a half wave dipole at the center feedpoint is close enough to 50 ohms to simply attaching a 50 ohm coax from it to your radio. Very convenient and simple. However it is limited to use on a single band, and for portable operation the extra length of coax needed to go from the elevated center of the antenna to your radio can be inconvenient. The EFHW on the other hand, performs as well, can be used on multiple bands and is fed at one end instead, requiring less coax and simplifying installation. Particularly in portable setups those two features can make it very attractive.
The main issue with feeding a half wavelength wire at the end rather than at the center is matching the several thousand ohms impedance to your 50 ohm transmitter antenna terminal. The rest of this page focuses on that issue. There are also some links to resources at the end of this page. A good video regarding the End Fed half Wave Antenna is by Steve Ellington. Click here to watch it.
One other note. One advantage of the end fed half wave antenna over an end fed "random" wire antenna is that it can be used on bands harmonically related to the band it is cut for without a tuner. So, one cut for 40 meters for example, can be used on 20, 15 and 10 meters without a tuner. To use it on 30, 12 and 24 meters does require a tuner.
Over-simplified, the primary physical difference between an EFHW and an end fed random wire antenna is the length of the radiator. As indicated above the EFHW is cut to a half wave length on the lowest frequency for which you wish to use it, around 60' for a 40 meter one. In contrast, an end fed random wire antenna must have its radiator cut to NOT be a half wave on any frequency for which you wish to use it, typically between 29' and 41'.
Another notable difference is the impedance a the feed point. The EFHW will be around 2500 ohms at resonance and often a 49:1 matching transformer is used to bring it close enough to 50 ohms so a tuner is probably not needed. The random length end fed antenna will be in the several hundred ohms range requiring a 9:1 transformer so the normal tuner can match it to the radio.
The primary advantages of an end fed random wire antenna over an EFHW antenna is that it is typically shorter AND with a tuner can be used on almost any band. It is however a compromise in terms of performance. However, because of its flexibility it may be worth the performance compromise in some situations. I have and use both antennas in different situations with success.
Both antennas have their place and do what they do, as well or better than most other simple antennas. They are both excellent for portable operations as they can be very small and light weight and setting them up is about as easy as you can get. The half wave version is also a very good permanent wire antenna. I currently use one as my primary home station antenna.