IOS

iOS, formerly known as iPhone OS, is the operating system for the Apple TV, iPad, iPad mini, iPhone, iPod touch. iOS has four abstraction layers: the Core OS layer, the Core Services layer, the Media layer, and the Cocoa Touch layer.[outdated?]

Name History
Initially, when the original iPhone was announced by Steve Jobs (on 2007), it was said to be running a variant of Mac OS X. This is presumably due to both OSes running on the Darwin/XNU kernel. After some time[when?], it was announced that the iPhone ran iPhone OS. This name was kept until version 4.0 when it was renamed to iOS.

For the next few years, the iOS moniker was used for the entire iDevice lineup of iPhones, iPod touches, iPads, and Apple TVs. With iOS 9, tvOS, a specialized version of iOS tailored for Apple TVs, was introduced. With iOS 13, iPadOS, another specialized version of iOS, but tailored for iPads, was introduced.

Size Growth
As new devices and frameworks come out, the /|root partition needs to hold more and more stuff. Consequently, Apple can't just add a separate NAND chip to hold the operating system as new releases would use more than available on the chip. As such, with each release, users get less and less usable storage space.

When jailbroken, Cydia "stashes" certain folders under the user partition to avoid filling the root partition when tweaks and apps are installed. However, Cydia doesn't shrink the root partition (and grow the user partition), so users get even less available storage space (e.g. if for a 16 GiB device with a 2 GiB root partition, Cydia "stashes" 1 GiB, the usable storage space will be 13 GiB). It is unknown if there exist tools to resize and move the partitions around in order to reclaim the empty space on the root partition (what was occupied by the stashed files).

Prior to iOS 4, the OS would take up ~350 MB of the device's storage on a 500 MB partition.

In iOS 4.0, it takes up ~800 MB of space, changing the root partition to 1000 MB due to the  graphics that have been added for the iPhone 4 (iPhone3,1) and iPod touch (4th generation) retina displays.

In iOS 5.0, Apple began pushing towards a computer-less experience for iOS. (e.g. devices can be activated and updated over the air.) In addition, multitasking gestures are now enabled by default. It takes up ~700MB for iPhone 3GS, ~800MB for A4 and A5.

In iOS 6.0, it takes up ~850 MB of space on the A4 and A5 series and ~1.2 GB on the A6 series.

In iOS 8.0, it takes up ~4 GB on the A7 series.

In iOS 10.0.1, it takes up ~3.9 GB on the A9 series.