So Americans use Z's because of nineteenth century dictionaries, while British people use S's because they're asserting their national identity.
In British English, s is generally used in such words as recognise, authorise. The letter z is used in American English in such words as recognize or authorize. However, it is not wrong to use z in such words when using British English as standard.
Much of our modern alphabet comes directly from the Greek alphabet, including a letter, that looked just like our “Z,” that the Greeks called “zeta.” “Zeta” evolved into the French “zede,” which in turn gave us “zed” as English was shaped by Romance languages like French.
When these Greek words were carried over into French, S was used to spell them. Since the sounds [s] and [z] are allophones in French of the same phoneme French had no need of the Z symbol. English tended to borrow these words from French and thus kept the spelling with S.
Why do the British use an 's' in words like 'realise' but the Americans use a 'z'? It's because American English spelling, many of the rules of which were devised by Noah Webster, who thought it would develop into a separate language, follows the rules of Latin and Greek, whereas British English uses those of French.
In most English-speaking countries, including Australia, Canada, India, Ireland, New Zealand, South Africa and the United Kingdom, the letter's name is zed /zɛd/, reflecting its derivation from the Greek letter zeta (this dates to Latin, which borrowed Y and Z from Greek), but in American English its name is zee /ziː/, ...
Zed is widely known to be used in British English. But it's also used in almost every English-speaking country. In England, Scotland, Wales, Ireland, Australia, India, Canada (usually), and New Zealand, Z is pronounced as zed. It's derived from the Greek letter zeta.
In short, the British pronounce “Z” as /zɛd/ (zed) whereas Americans pronounce it as /ziː/ (zee). Note that the same pronunciation is naturally used also in the plural: the plural of “Z”, denoted “Zs”, “Z's” or “z's”, is pronounced as /zɛdz/ (zedz) in the UK and /ziːz/ (zeez) in the US.
Mom and Mommy are old-English words, words that are stilled used in Birmingham and most parts of the West Midlands. It is said that when people from the West Midlands went to America many years ago they took the spelling with them, hence Americans use Mom and Mommy.
English zucchini goes by courgette in England, the French word for the green gourd. The United States inherited the Italian name, and both terms reference the summer squash. Note that the word squash refers to a fruity drink in Britain, and a mature version of the courgette fruit becomes marrow.
The UK version is more logical. Math is an abbreviation of mathematics, which is a count noun in British English because there are different types of maths (geometry, algebra, calculus, etc.) and a mass noun that happens to end in an 's' in American English (like gymnastics in both dialects).
Over time the word "locum" evolved into the French word "lieu", which is pronounced in French as it is spelled. It is possible that when the English heard the French pronounce the compound word lieutenant, they perceived a slurring which they heard as a "v" or "f" sound between the first and second syllables.
Gray and grey are both common spellings of the color between black and white. Gray is more frequent in American English, whereas grey is more common in British English. The varying usage of both grey and gray extends to specialized terms such as animal species (gray/grey whale) and scientific terms (gray/grey matter).
Center is the correct spelling in American English, while in British English, centre is correct. Notice that center (and centre) can be a noun, adjective, or a verb.
More commonly people refer to their parents as their mom in US English, or mum in UK English, and their dad in both UK and US English. These words are more informal than mother and father. US His eyes filled with tears when he saw his mom and dad. UK My mum and dad go there every year.
The modern English 'mother' comes from the Old English term modor. As such, it is also where many of our informal terms for mothers come from, from 'mommy' and 'mumsy' to 'ma' and 'maw'.
Russian state
Since mid-March 2022, the "Z" began to be used by the Russian government as a pro-war propaganda motif, and has been appropriated by pro-Putin civilians as a symbol of support for Russia's invasion.
The American Chemical Society (ACS) officially adopted aluminum in 1925, but in 1990 The International Union of Pure and Applied Chemistry (IUPAC) accepted aluminium as the international standard. And so we land today: with aluminum used by the English speakers of North America, and aluminium used everywhere else.
Sometimes the z is pronounced like in the english word "zone" or "zebra" like in 水, other times it is pronounced more like a "dz"for example in 雑誌 (ざっし) or 全部.