According to Hans Wehr:
الحقيقة: truth, reality, fact.
الحَقّ: truth, correctness, rightness, etc.
These two words are very similar in meaning, sound similar, and have the same root letters (ح ق ق). Thus, it is no surprise that the two are often mixed up. Even Hans Wehr’s first definition of both words is “truth”. So what is the difference?
الحقيقة: This is referring to the essence of something, that which constitutes the identity of a thing.
Ex: The essence of a chair is that it has 4 legs and place to sit on. Everything else would be considered a characteristic of it.
*It is also something that can either be good or bad.
الحَقّ: This is something that is associate with wisdom, and thus can only be associated with good things.
This is why the Quran says:
هُوَ الَّذِي أَرْسَلَ رَسُولَهُ بِالْهُدَىٰ وَدِينِ الْحَقِّ لِيُظْهِرَهُ عَلَى الدِّينِ كُلِّهِ وَلَوْ كَرِهَ الْمُشْرِكُونَ
“It is He who sent His Messenger with guidance and the religion of truth to manifest it over all religion, although those who associate others with Allah dislike it.”
*It can also be understood as when the reality of something is in accordance with what is being stated.
In summary: الحقيقة is the “true” nature of something, while الحَقّ is the embodiment of “truthfulness”, good, and correctness.