For me, and I believe to the majority of Greek Cypriots, unity means a one country one people kind of unity. So that the end result will be one country like one country is UK, France, Turkey, Bulgaria, Russia etc.
However I came to the unfortunate conclusion that for the majority of TCs the word "unity" means some sort of EU unity within Cyprus, so that "North" and "South" will be "united" more or less in the way that Italy and Finland are "united" within the European Union.
Here are some of the factors that made me come to this conclusion:
1) TCs insist that the northern part of our country is their own. All they accept is to allow a small GC minority within "their" state/"country". This can not exist in a single united country. Even in Federations (e.g. USA, Russia) people are free to move and become residents with full rights of any state they want.
2) They insist on a power sharing scheme that exists only in associations of separate independent countries. For example when I tell them the obvious, that it is undemocratic to have 18% people having 50% power and a veto power on everything, and I ask them to give me another country were such thing exists, the example they usually come up with is the one of EU saying something like "how can Cyprus then can have a veto in EU". This is another clear indication that the kind of "unity" they want is one between separate countries as it exists within the EU countries and not a one country kind of unity.
3) They insist on things like "rotating presidency" between the two communities. Such thing exists only in separate country associations (e.g. EU) and not within single countries.
4) Not many of them seem to be bothered by the "trnc" which in affect pretends to be a separate country within Cyprus, and many of them even see "unity" as the cooperation of "trnc" and Republic of Cyprus.
I believe that TCs that understand "unity" more or less as described above are the great majority of them. Then there is a minority which doesn't even want any kind of association with the "south" (e.g. Denctash) and another minority which includes people like Sevgul Uludag who want a one country unity.
Here is again a quote from Sevgul which is relevant to how the majority of TCs realize "unity"
The main problem concerning `reunification` of the island for the mainstream Turkish Cypriot media is that it is subconsciously based on `two separate entities coming together`, not seeing that this is a remnant of `Taksim` policies… The focus is on `Bizonality` and with this, the `legitimization` of `the results of 1974`… No one is contesting that any future cooperation of our communities should be based on multiculturalism, rather than on the `hegemony` of the Greek Cypriot community in all fields… But how `bizonality` is perceived is a big problem because deep down, the ideology of `Taksim` is still there and has not been wiped out from the subconscious thinking of `duality` and `separatism` from the minds of some mainstream Turkish Cypriot journalists.
As I said many times before the first step for any agreed solution is agreeing on the aim. If we both say "unity" and we mean two totally different things, then how could a solution that will be accepted by both sides ever be found?