What’s the correct use of “last/late/latter/latter” in time expressions?

Solution 1:

The term late is an adjective and has got two forms in terms of "time and order"

Late (time) –>later –>latest
Late (order) –>latter –>last

When it is a matter of time it suggests the point in time e.g., “The latest discoveries (the most recent discoveries) of genome has startled the world” as compared to "later" (before the latest discoveries) “…in the same domain, nonetheless, research started "late" in the 19th century.”

When it is a matter of order it suggests the position e.g., “George had a heated argument with Smith which resulted in physical clash, but latter (Smith) ran off in last”

Hope it will help you