Given the following examples from Oxford Dictionaries
1) ‘I glowered, having a strong urge to turn away from him, but I knew that he intended well.’
2) ‘Larenia giggled after she finished saying this and I had the strong urge to giggle with her.’
What is the difference in meaning between the noun phrase "a strong urge" in the first example and the noun phrase "the strong urge" in the second example? Namely, why in the first example we have "a" and in the second example we have "the" before the noun? Does it make any difference?