exist, outskirts, suburbs, located in
在 centers on being present in a place or state: existing, being located somewhere, or being in the outskirts/suburbs of a city.
在 combines 才 (a phonetic element suggesting presence) with 土 (earth/ground), together conveying the idea of existing or being situated in a place.
The top-left part looks like a simplified person or marker, and the bottom 土 is the ground. Picture a person standing on the earth, marking where they exist.
For ザイ, imagine a sign saying 'I exist here' written in bold, like a 'ZAI' stamp on the ground: ZAI -> ザイ.
existence; being; presence
the present; present time; now
stay; sojourn
stock; inventory
resident in Japan (of a foreigner); situated in Japan (e.g. of an embassy)
residing; living; dwelling
actual existence; real existence; existing in real life
being enrolled (at a school); being registered; being a member (of a team, organization, etc.)
potentiality; dormancy; latency
absence
location (of); position; whereabouts; place where one is
location; address
being at home; being in
being able to do as one pleases; doing at will
in good health; alive and well; going strong
attending (school, college, etc.); being enrolled; being a student
pre-existing; already there; conventional
residing (esp. abroad); staying; living
being dotted about; being scattered; being interspersed
residence; stay; (job) posting; being stationed (overseas, etc.)
being actual (as opposed to hidden or latent); being apparent; being obvious; being tangible; being revealed
being in office; holding a position; employment; service
existing (between); interposition; intervention; involvement
being in office
overseas; abroad
being in the capital (i.e. Tokyo, or formerly Kyoto)
staying in the United States; residing in the United States; being situated in the United States (of a foreign embassy, company, etc.)
out of office; out of power; in opposition
absentee ballot; absentee voting
past days; bygone days; days of yore; the olden days
diplomatic mission; overseas diplomatic establishment
during a stay