The Chinese cultural sphere include mainly countries using or having used Han script, that is China (Mainland and Taiwan), Japan, Korea, Viêt Nam, and few other countries where Chinese is an important language; Malaysia and Singapur.
漢字 or in simplified shape 汉字 (hanzi in modern standard Mandarin Chinese, one of the several Han languages among Chinese languages), meaning Han (ethnie) script is the script of the main Chinese population, in China for several milleniums. There are not hyeroglyphs (Egyptian script), even if they have in common, as most of all of the planet scripts, pictographic origin.
Beside China, the Han charactees was also the main script used in Koreas (漢字 hanja), Japan (漢字 kanji) and Vietnam (漢字 Hán tự) until the middle of 20th Century. They are often called CJK instead of CJKV, don't know why, Korea as Vietnam don't use them anymore in their everyday script, Vietnam still used it officialy until 1954, the time of French decolonization, where Korea, if I'm not wrong stopped to use it with japanese decolonization in 1945.
Inside 18th and 19th Century China, Mongolians and Tibetan used, probably due to Manchu influence all over China, decoration with rounded shape longevity han character (寿 shou, some thinking that's the near rounded character happiness), also used as first character to describe sushi (寿司) in Japan. They are still used today in independant Mongolian Republic, or by Mongolians of China and Russia too, and by Tibetans, or several mixed culture of Tibetan, Mongolians, Turkic or other minorities cultures.
Japanese uses several Han languages pronunciation for it's Han script (on'yomi) and several specifically japanese pronunciation (kun'yomi). Chinese pronunciation don't come from modern standard Mandarin, but from 3 distinct periods, including Tang dynasty, when monks bring chinese culture (including script, agriculture, painting, music, etc) to Japan, and the Mongolian (from futur Yuan dynasty) invasion toward the Song dynasty, when people flyied from around Hangzhou (Wu languages, called Go in Japanese) to Japan (as example, isha 医生is similar to some parts of today Wenzhou languages).
Still studied at school, still displayed on monuments and during festival, Korean people (from both Jilin and Liaoning province in China, North Korea and South Korea), all use hangeul or hangul now to write Korean everyday.
The last system was created during middle-age, probably derivated from Phagpa scrpt, used by Mongolian during their rule on China, Yuan dynasty, it was quickly blocked by kings, after too much people learned to read ansd write. It come back at the end of the 19th century, and become the main used script during Japanese colonisation of Korean peninsula.
Korean han script wasn't really different than Chinese or Japanese variants. Only few characters have some minimal differences.
This script also have several other names in Viêt Nam: (𡨸儒, Chữ Nho, meaning scholars script), (chữ Hán (𡨸漢, han script with proper Vietnamese grammar), (chữ Nôm, 𡨸喃, South Script, that diverged the most from han script, since 11th century, with far more differences than Korean or Japanese han scripts). They build a bunch of new characters, by still following Han rules of characters construction.
Han script was offcially used in Viêt Nam until 1954, they made the biggest changes in Chinese script from 11th century, date of their independency from China, until colonization by France. France, then teached latin script to children at schools, but kept Han script at the same time as official script. Every official document during this period, had both French, Han vietnamese and latin vietnamese. After the independency, The communist governement only kept latin script. Han script is still used by scholars, and probably some confucean followers.