Intimacy, n.; pl. Intimacies.
Etymology: [From Intimate.]
The state of being intimate; close familiarity or association; nearness in friendship.
Syn. -- Acquaintance; familiarity; fellowship; friendship. See Acquaintance.
Shades of meaning
Fernald has no entry of its own for intimacy; he lists it under acquaintance.
Where he writes about it:
So there may be association in business without intimacy or friendship. — from acquaintance
Acquaintance admits of many degrees, from a slight or passing to a familiar or intimate acquaintance; but acquaintance unmodified commonly signifies less than familiarity or intimacy. — from acquaintance
As regards persons, familiarity is becoming restricted to the undesirable sense, as in the proverb, "Familiarity breeds contempt;" hence, in personal relations, the word intimacy, which refers to mutual knowledge of thought and feeling, is now uniformly preferred. — from acquaintance
Friendship includes acquaintance with some degree of intimacy, and ordinarily companionship, though in a wider sense friendship may exist between those who have never met, but know each other only by word and deed. — from acquaintance