1.3.5.2 Determiners
In the first sentence there is a specific cat that I am looking for, and the speaker obviously assumes the person who is addressed knows which specific cat he is talking about. The second sentence is, however, ambiguous. It could either mean that the speaker was looking for a specific cat, but assumed that the addressee does not know which cat is referred to, or it could mean that the speaker is looking for some non-specified cat and that any cat would satisfy the conditions of his search.