Later is after in time. Latter is the second of two things just named. See you later. Tea or coffee? The latter. Diction as a set is in word choice.
Time versus the second one
If you can swap in afterward, use later. If you can swap in the second of those two, use latter. The later of the two options is the usual miss.
Quiet versus quite is another look-alike pair, in quiet versus quite. Then versus than is in then versus than. Grammar overall is in ACT grammar rules.
The bottom line
Afterward: later. The second of two: latter.
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