Do people really distinguish "Strong Eventual Consistency" from "Eventual Consistency"? To me, when I say "Eventual Consistency" I alwayes mean "Strong Eventual Consisteny".
In an eventually consistent system replicas can diverge. A "last write" system can be eventually consistent, but a given point can read differently.
Eg: operations
1) Add "AA" to end of string 2) Split string in middle
Replicas R1 and R2 both have the string "ZZZZ"
If R1 sees operations (1) then (2) it will get "ZZZZAA", then "ZZZ", "ZAA"
If R2 sees (2) then (1) it will get:
"ZZ", "ZZ", then "ZZAA", "ZZ".
Strong Eventual Consistency doesn't have this problem because the operations have the time vector on them so the replicas know what order to apply them.
But the point is that there is a point in time where reading from different replicas gives different results.
In the CAP theorem consistency is comprised.
Any eventually consistent system has to have a strategy for ensuring that all nodes eventually agree on a final value. R1 and R2 need to communicate their respective states, and agree to a single one of them - maybe using timestamps if R2's value is newer, R1 will replace its own value when they communicate), maybe using a quorum (say there is also an R3 which agrees with R1, then R2 will change its value to match the other two), maybe using an explicit priority list (say, R1's value is assumed better than R2's).