CROSS APPLY produces outer join

In answer to https://dba.stackexchange.com/q/239788 Erik Darling posted this code to work around for the lack of COUNT(DISTINCT) OVER ():

SELECT      *
FROM        #MyTable AS mt
CROSS APPLY (   SELECT COUNT(DISTINCT mt2.Col_B) AS dc
                FROM   #MyTable AS mt2
                WHERE  mt2.Col_A = mt.Col_A
                -- GROUP BY mt2.Col_A 
            ) AS ca;

The query uses CROSS APPLY (not OUTER APPLY) so why is there an **outer** join in the execution plan instead of an **inner** join? Also why does uncommenting the group by clause result in an inner join? I don't think the data is important but copying from that given by kevinwhat on the other question:

create table #MyTable (
Col_A varchar(5),
Col_B int
)

insert into #MyTable values ('A',1)
insert into #MyTable values ('A',1)
insert into #MyTable values ('A',2)
insert into #MyTable values ('A',2)
insert into #MyTable values ('A',2)
insert into #MyTable values ('A',3)

insert into #MyTable values ('B',4)
insert into #MyTable values ('B',4)
insert into #MyTable values ('B',5)