The only technical difference that I see is that the crossing operation would create a unique page s. The first can generate duplicates.
Update: They are not the same. the correct answer is what Dems has already explained (I voted for his answer):
page word part 1 france headline 2 uk headline 2 france body
word = france AND part = headline => page 1
word = france => page 1, 2 part = headline => page 1, 2
intersection of the previous two sets => p. 1, 2
Update2: The answer to the question: how to make intersect give the same result? The intersection should be performed on the column under conditions like here.
select page, word, part from title where word = 'france' intersect select page, word, part from title where part = 'headline'
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