Do these devices do the same thing?

For the metal shed, I would bury an outdoor rated Ethernet CAT5e cable (best in 1/2 inch PVC conduit to protect it from digging and creatures) and stick a router configured as an AP inside the metal building. Metal sheds are very hard to penetrate, so it is best to have the AP inside the shed.

I would use outdoor AP with high power Ubiquiti Networks directional antennae, for the distant locations.

You are near the limit of a radio like that even if the far end was outdoor you will likely not get enough signal inside any building. You would have to use a outdoor antenna on the far unit or run a cable as suggested.

To go the longer distance you will have to use directional equipment on both ends. The electronics are pretty cheap your problem is what is called freznel zone. This is related to the spread of the signals and how much the ground absorbs over distance. Without doing the math I am going to bet you are going to need to be 30ft above the ground on both ends. That assumes no other large structures or tall trees in the way. You can get self supporting 30ft towers for about $600 but you will spend another few hundred for concrete assuming you dig the hole and mix it all yourself.

Be nice if manufacture had not decided to steal the term PoE for something other than the standard 802.3af. Most the time if it uses a non standard form of PoE it will have the adapter. Some that use standard forms of PoE come with adapters. They are not real expensive in any case most people just buy small switches that have the feature when it uses standard 802.3af form of PoE.

The word coverage is very much abused by manufactures. Some mean the signal is detectible and other mean you can connect but at extremely low speeds.

The central location is only half your problem. What you are connecting to on the far end makes a huge difference. A cellphone that uses low power to conserve battery, or a laptop that can move around, or a fixed router/bridge device all have different requirements.

So to start in the central location it depends how many directions you must transmit. If you must support 360 degrees it is much harder. The simple solution is the omni directional antenna but when you use these they spread the power out in all directions so they do not have the same distance. If you can transmit to only a single direction you can use narrow beam antenna that concentrate the power which increases the range in that one direction...of course it greatly reduces it in all others.

On the far end you have the same issue and almost all antenna that are used on end devices are omni directional and somewhat limited in their size.

The number used by most people in the industry is 300ft for a outdoor unit with omni directional antenna talking to omni direction antenna on the far end.

You get more distance if you can put direction units on either end. On the central side you could use a cluster of 4 directional units that cover a 90 degree each. I would guess you could get the 600ft if you had directional on at least one end....but this is just my guess without doing all the complicated math.

Now the optimum distance is achieved when you can concentrate the signal into a very narrow beam on both ends. In addition the government rules on transmission power are more lenient when you are running point to point. This is how they get those units that can go many miles. The problem though is the radio waves are concentrated into a much narrow path and if anything is in that path it tends to block more also. Also when you go long distances you get problems related to the curvature of the earth that make no difference when you are going a few hundred feet.

This is a extremely complex topic, people get degrees in RF engineering to do work like this and are being hired by cell phone companies before they even graduate.

The Ayrstone AyrMesh Hub2n is the same hardware as the Ubiquiti PicoStation M2HP - the difference is in the firmware. I run Ayrstone, so I can speak pretty authoritatively on this.

The Ubiquiti AirOS firmware is designed for a WISP tech - it has pages of options to help a tech integrate the device into an existing network, as well as Ubiquiti's cool AirMax TDMA mode (which I believe is unique to its products). It can be configured as an access point or a client; it does not, however, do meshing.

The AyrMesh Hub is designed for a farmer - it has no options, is self-configuring from Ayrstone's cloud-based management and monitoring system, and is all standard 802.11 (specifically, s for meshing and n/g for the access point). It is designed for use in rural settings (farms, ranches, etc. - "radio quiet" locations) with a relatively small number of client devices (tens per "Hub") spread out over a large area (many, many square miles).

The Hubs, if placed high and in the clear (25' above any obstructions) and in a quiet (rural) location can mesh effectively up to 2.5 miles apart, and you can "chain" them out up to 3 "hops" in every direction (bandwidth is halved at each "hop"). Therefore, you can cover an circular area up to 7.5 miles in radius with AyrMesh Hubs.

WiFi is UHF radio, and the "rules" of UHF radio are complex (and may require, quite literally, complex math), but the most important one is this: 60% free Fresnel Zone. As long as you can have a 60% free Fresnel zone and little RF interference, 2.4 GHz radio transmission (e.g. WiFi) is relatively easy, with the actual range determined by the power of the WiFi radios and the gain of the antennas. Trees, buildings, hills, rocks, etc. are impediments to the 60% Fresnel zone, and towns tend to be very "radio noisy," so we market the Ayrstone products solely to rural homes and businesses, and include as much information as we can about their proper placement.

Power and antenna gain help, of course. In the U.S. and Canada, an Access Point (point-to-multipoint) can have up to 30 dBm of power (1 watt, about the same as a good LED flashlight) to a 6 dBi antenna (directional or omnidirectional). The Ubiquiti PicoStation/AyrMesh Hub is rated at 28 dBm +/-2 dBm (so, effectively, 30 dBm) and comes with a 6 dBi antenna, so it's the most powerful WiFi radio that's legal. Some countries have much lower power limits.

Finally, 802.3af is a good thing, but requiring 44 volts makes it hard to power things from solar cells and batteries. If you're going to put stuff far from the electrical grid, it's good if they run well on 12 volts, which the PicoStation or Hub does nicely.

For the adventurous, I advise getting some PicoStation M2 units, flash them with OpenWRT, and mess around! Open80211s, OLSR, and Batman-adv are integrated into OpenWRT, and there is much that can be done and learned with them - that's essentially what I did. And I kept messing around until I came up with a "recipe" that solved the problem I was looking at: providing an IP network across a farm, ranch, or other rural property.

For reference: Ubquiti is http://ubnt.com and Ayrstone is http://ayrstone.com