Sorry this is a bit long, but there's a lot to explain.
But countries and borders are changing throughout history. Look at Germany - Germany 1982 is completely different from Germany 2010. Why is this the same winner according to your logic?
If you wanted to be really pedantic about Germany, the EBU could say the following:
1) West Germany participated from 1956 to 1990, won for the first (and only ever) time in 1982, and thus hosted it from Munich in 1983. From 1991 onwards it no longer existed as a nation.
2) A new country Germany (which didn't exist prior to 1991) had its debut entry in 1991, its first ever win in 2010 and hence hosted it from Dusseldorf in 2011.
But they don't. Even though sometimes I saw Germany shown as West Germany in the 1980s (e.g. in a newspaper article about the ESC), as far as the EBU is concerned, it's always been Germany from 1956 to 2012, and has had two wins (1982, 2010). Take a look at the eurovision.tv
Germany page and it lists all Germany's entries from 1956 to 2012. The official name for West Germany was FRG - Federal Republic of Germany (Bundesrepublik Deutschland), and still is since reunification of Germany late 1990. Presumably that's why as, as far as the EBU are concerned, West Germany (1956-1990) and Germany (1991 to-date) are the same country. East Germany, aka GDR - German Democratic Republic (Deutsche Demokratische Republik), never took part in the ESC, and ceased to exist when Germany was reunited on 3 October 1990.
And Serbia-Montenegro was the legal successor of Yugoslavia until 2006, because all the other countries abandoned Yugoslavia. But Croatia was the representative for Yugoslavia in 1989... Actually Yugoslavia was the other name for Serbia and Montenegro.
The history of Yugoslavia ends in 2006, when Serbia and Montenegro split up to become independent countries.
Yugoslavia in the Eurovision Song Contest is quite a tricky issue, and here's an
interesting page on Wikipedia about it. According to that, the Socialist Federal Republic of Yugoslavia participated in the ESC from 1961 to 1991 under the name
Yugoslavia, won once in 1989, and hosted it from Zagreb in 1990.
The breakup of Socialist Federal Republic of Yugoslavia happened during 1991 (after the 1991 ESC). By the time of the Yugoslav national final Jugovizija 1992, Croatia, Slovenia and Macedonia had already broken away from SFR Yugoslavia and didn't take part in Jugovizija 1992. However entries from Bosnia and Herzegovina, Montenegro and Serbia entered. The winner, which went on to represent "Ljubim Te Pesmama" - Extra Nena in the ESC on Saturday 9 May 1992 was from Serbia. In the interim period, Bosnia & Herzegovina gained independence on 1 March 1992, and what was left of SFR Yugoslavia (an area equivalent to the later Serbia & Montenegro) became officially known as Federal Republic of Yugoslavia on 28 April 1992. I've seen from another source that Extra Nena's "Ljubim Te Pesmama" ended up representing just the then new country Federal Republic of Yugoslavia, albeit still under the name
Yugoslavia, in the ESC 1992 on 9 May 1992. From 1993 onwards, Federal Republic of Yugoslavia was excluded from the ESC for some reason, one reason I've seen somewhere was that JRT ceased to exist by 1993.
In 2003 Federal Republic of Yugoslavia was reconstituted as a political union called State Union of Serbia and Montenegro. From what I can gather of that, Federal Republic of Yugoslavia (an area equivalent to Serbia and Montenegro) was one country from 1992 to 2003, whereas State Union of Serbia and Montenegro was a loosely coupled pair of two states from 2003 to 2006. So you see, Federal Republic of Yugoslavia and are evidently not quite the same thing. Effectively therefore, Yugoslavia officially ceased to exist in 2003 at the time of the said reconstitution. The State Union of Serbia and Montenegro first entered the ESC in 2004, and had its last ever entry in 2006 (though that year it withdrew last minute but still voted in the grand final). Serbia and Montenegro became fully independent in June 2006, and took part in the ESC as two new countries in 2007.
If the EBU wanted to be really pedantic about Yugoslavia and its component countries in the ESC 1961 to present, they'd have done the following:
Socialist Federal Republic of Yugoslavia (under then name
Yugoslavia): first entry 1961, last entry 1991, had just one win in 1989 and hosted the Contest in 1990.
Federal Republic of Yugoslavia (under the name
FR Yugoslavia to make it clear it was a new, different country to the previously mentioned Yugoslavia): first (and only ever) entry 1992, never won or hosted ESC in its short lifetime.
Croatia: first entry 1993, no wins to-date.
Bosnia & Herzegovina: first entry 1993, no wins to-date.
Slovenia: first entry 1993, no wins to-date.
F.Y.R. Macedonia: first entry 1998, no wins to-date.
State Union of Serbia and Montenegro (under the name
Serbia and Montenegro): first entry 2004, last entry 2006, never won or hosted ESC in its short lifetime.
Serbia: first entry 2007, first win 2007, hosted ESC 2008.
Montenegro: first entry 2007, never qualified from semi-final to-date.
The Yugoslavia / Serbia & Montenegro issue is a rather hot topic, in particular the 1992 Yugoslavia entry "Ljubim Te Pesmama" - Extra Nena. Some argue it's really Serbia & Montenegro's first entry rather than Yugoslavia's last entry; indeed the Diggiloo Thrush actually lists it on the Serbia & Montenegro page.
As far as I'm concerned, the only official source for ESC history by year and country is the official ESC site
Eurovision Song Contest - Baku 2012 Take a look at the
History By Country page. It lists Yugoslavia as having its first entry in 1961, and one victory (1989). Croatia is listed as having first entered in 1993, and no victories to-date. It even shows Serbia & Montenegro as a country in its own right, 3 entries altogether, first entry 2004, no victories. Serbia is a separate country on the list, first entry 2007, one victory 2007.
If you look at individual country pages you will see:
Yugoslavia: all entries from 1961 to 1992. Yes the 1992 Yugoslavia entry, Extra Nena - "Ljubim Te Pesmama"
is on the Yugoslavia page, not the Serbia & Montenegro page, so it is Yugoslavia's last ever entry as far as the EBU is concerned.
Croatia: all entries 1993 to 2012.
Serbia & Montenegro: 2004 to 2006. It actually menions the 2006 withdrawal.
Serbia: 2007 to-date.
So it appears that, as far as the EBU is concerned, Yugoslavia's only win in 1989 still belongs to Yugoslavia (which for statistical purposes is a country that no longer exists), not Croatia.
You've got to remember the ESC has been going for over 50 years. Some countries that entered (e.g. Yugoslavia) or perhaps in theory could have entered (e.g East Germany, USSR) but never did don't exist any more, simple as that. Many present-day eastern bloc countries that have debuted since 1993 (ex-Yugoslavia and ex-USSR countries) didn't exist as independent countries when the ESC started in 1956.