Difference Between FOR INSERT And AFTER INSERT Triggers

I've been reading the docs and playing around, but I'm still not
getting the difference. For instance,

create table a(i int check(i>0))
create table a_src(i int)
go
create unique index ai on a(i) with IGNORE_DUP_KEY
go
insert into a_src values(1)
insert into a_src values(1)
insert into a_src values(2)
--insert into a_src values(-1)
go
create trigger a4ins on a
for insert
as
select * from inserted
go
create trigger afterins on a
after insert
as
select * from inserted
go
insert into a select * from a_src
go
drop table a
drop table a_src


I'm getting

i
-----------
1
2

(2 row(s) affected)

Server: Msg 3604, Level 16, State 1, Procedure a4ins, Line 4
Duplicate key was ignored.
i
-----------
1
2

(2 row(s) affected)

even the inserted quasi tables are identical.
If I uncomment insert into a_src values(-1), I'm getting

Server: Msg 547, Level 16, State 1, Line 1
INSERT statement conflicted with COLUMN CHECK constraint
'CK__a__i__58FC18A6'. The conflict occurred in database 'ABC_1COMPEE',
table 'a', column 'i'.
The statement has been terminated.

without any output from either trigger.
So,
in which situations will FOR INSERT be useful while AFTER INSERT won't
do?
in which situations will AFTER INSERT be useful while FOR INSERT won't
do?