How to select distinct rows group by

SELECT DISTINCT date,message FROM table

or

SELECT DISTINCT DATE(date),message FROM table

(I am assuming the date field is not really called date)

Hello Arne,
Thanks a lot, but I did not gave you the whole picture, as usually.Sorry for that.
It may look like this
1, x, 2019-08-26 12:44
2, x, 2019-08-26 12:45
3, x, 2019-08-26 12:46
4, y, 2019-08-26 12:47
5, z, 2019-08-26 12:48

I need to select to get a result like this:
x, 2019-08-26
y, 2019-08-26
z, 2019-08-26

Best regards
Fredrik

And:

SELECT DISTINCT DATE(date),message FROM table

doesn't do that?

Hello Arne,
That question gave me a list like:

2019-08-26 16:00    x
2019-08-26 16:01    x
2019-08-26 16:03    x
2019-08-26 16:06    x
2019-08-26 15:55    y
2019-08-26 15:54    y
2019-08-26 15:58    y
2019-08-26 15:58    y

Could this be since there probably is some millisec that makes each row unique?

Aha, wait minute I think I missed DATE(date), back in a minute

Hmm... my Oracle seems not to like the DATE()-call.

So would you say that this is wrong (it gives my duplicate rows like above):

SELECT DISTINCT(tidpunkt), meddelande FROM my_table;
WHERE
    tidpunkt between sysdate-10 AND sysdate
AND
      meddelande like '%MyMeddelande%'
ORDER BY meddelande;

Btw tidpunkt is a Date,

Sorry but missed to remove a semicolon.Sorry for spamming!
So would you say that this is wrong (it gives my duplicate rows like above):
SELECT DISTINCT(tidpunkt), meddelande FROM my_table
WHERE
    tidpunkt between sysdate-10 AND sysdate
AND
      meddelande like '%MyMeddelande%'
ORDER BY tidpunkt;

Btw I do not I think it is possible to just get it per day if there are several rows spread among a day at different times.

Nyt forsoeg:

SELECT DISTINCT TO_CHAR( tidpunkt, 'YYYY-MM-DD'), meddelande FROM my_table
WHERE
    tidpunkt between sysdate-10 AND sysdate
AND
      meddelande like '%MyMeddelande%'
ORDER BY TO_CHAR( tidpunkt, 'YYYY-MM-DD');