I'm planning to to start my travel in Barcelona and then head off to Greece, Santorini.
Do I have to apply for a separate Schengen visa for Greece? I'll stay longer in Barcelona.
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No, both countries are in the Schengen area, you do not need separate visas for them. The one visa you should apply for must be valid though for the whole period of time you're planning to be in the Schengen zone. In case you're leaving the Schengen area and coming back during the trip, it has to be a multiple-entry visa. Give the whole itinerary with details to the embassy when applying for a visa to make sure you'll get one that satisfies your requirements.