Why some can be really thirsty without the frequent urination, or how can some have frequent urination without the extreme thirst?

Different situations: It is not the frequent urination that stimulates thirst but the amount of urine. If you loose lots of urine( in certain conditions), that makes you dehydrated which stimulates thirst. Any condition that results in the body loosing fluid; sweating, diarrhea, will also cause thirst. In addition high salt intake stimulates thirst. In summary thirst is the way our body protects itself from dehydration