Airships are a staple of Final Fantasy. Airships have had a fluxuating role in the series, with the first game introducing it late in the game while II treats it more akin to an airtaxi, the party only gaining full control over it late in the game. Final Fantasy III sets up the use of airships as something of a railroading element: The party gets access to numerous airships over the course of the game, but can only freely explore the world late in the game. In particular, III has an odd quirk where airships can't fly over mountains, even by the end of the game, which is used prevent players from reaching certain areas too soon.
The very first airship the party gets access to is Cid Haze's personal airship. Cid buried it in the nearby desert while visiting Kazus, and with the Djinn's curse turning him and everyone else in town into a ghost, he tells the Warriors of the Light where they can find it.
Cid's airship is primarily a tease. It makes moving around Inner Sasune much easier and is required to reach the Sealed Cave as it's blocked by a lake and the orphans have yet to get the canoe that otherwise allows them to cross. However, because Inner Sasune is surrounded by mountains, the airship cannot leave that area. By the time it's time to leave, the ship is outfitted with a Mythril Ram and then crashed upon the boulders bloking Nelv Valley: The path is cleared, but the airship itself is totaled.
The ship has an interior that is only seen when initially entering it. In the remake the interior is seen a bit more in the scenes where Refia joins and rejoins the party. In terms of design, the original had metallic walls and wooden flooring while the remake has more wood.
The remake establishes that Cid had an airship that he used as a taxi service back on the surface. However, the airship was destroyed in the crash onto the floating continent.
The Enterprise is a viking ship that becomes the Warriors of the Light's primary mode of transport after they calm the Nepto Dragon. Initially, it is an average boat, the last that the vikings had, and thus the Warriors of Light can only access the inner regions of the Floating Continent, although the edge of the continent can be reached. The few remaining key areas become accessible after clearing the Tower of Owen, but it's only after Hein has been defeated in his castle that the Warriors receive the means to leave the Floating Continent.
King Argus gifts the orphans the Wheel of Time, a perpetual motion device that is key in constructing airships. Bringing it to Cid allows him to transform the ship into an airship. The Enterprise remains the group's main vessal until they reach Saronia, at which point they are shot down, destroying the airship and trapping them in the city.
The name "Enterprise" has been used for numerous ships (hence Star Trek's Enterprise being named for a similar reason). The Enterprise is the first named airship in the series and it would be used again in Final Fantasy IV as the first airship the party gets access to.
The Nautilus is the third airship that the party gets, this time after saving Saronia from Garuda's machinations. Unlike the previous airships, the Nautilus' design is more heavily based on real life airships such as dirigibles. This design element would be reused for Final Fantasy VI's airships.
The primary selling point of the Nautilus is its speed: It is the fastest airship in the game with no equal. This is important as the Nautilus is fast enough to pass through the strong winds of the Dalg continent, allowing the party to reach Doga's Manor and kick off the final fourth of the game. After finishing the Cave of the Circle, Doga enhances it with the ability to go underwater, allowing the party to reach the Temple of Time as well as a few other secret spots. It is for this reason that the Nautilus never truly loses its use, even after the party receives their final airship.
The Nautilus' interior is the most mysterious of the three. In the Famicom version, it's only ever seen during the ending sequence, after the party returns Alus to Saronia. The remake uses the same "above the deck" background as battles during the ending, meaning the interior goes unseen entirely.
While the Nautilus is a creation of the Ancients, the 3D remake adds a connection to Cid Haze: Namely the implication that he resurrected it after it was discovered in the Ancient Ruins. The english version mistranslates this, however, causing the scholars to speak of an inventor from the "Saronia of old".
The Invincible is the fourth and final airship that the party receives. It is found deep in the Ancient Ruins, the path to it having a huge boulder that the party requires Unei to destroy. Once inside, Unei explains the various features of the ship before leaving.
The Invincible is the first "mobile base" airship in the series: An airship that's big and has amenities that allow the party to rest and store items outside of towns. More specifically, the Invinible has a bed (functions as a free inn) a shop and a space to call the Fat Chocobo. The remake further adds a moogle for Mognet, with later versions adding another to check the beastiary. On the field, the ship has two support features. First, it can jump over small mountains, allowing the party to reach Falgabard, the Cave of Shadows and Bahamut's Lair. Second, during random encounters, the Invinicble will open fire on enemies, supporting the party.
The Invincible went through several aesthetical differences between versions. In the original, the Invincible's sprite was based on the Dreadnought from Final fantasy II, although having subtle differences even then. This became the basis for the Invincible's exterior in the remake and the Pixel Remaster, although like Sasune and Cornelia, the Dreadnought had been redesigned at that point. The interior also got some changes in the remake: The vending machines were replaced with representations of each product along with a scale, implying that the shop is more mystical in nature, the Fat Chocobo is now in the center back of the airship and in-turn the single bed was moved to the middle and replaced by a small living area with a table and four beds.