Hello. You did not enter the text to which this question refers, which makes it very difficult to answer it exactly. However, I will try to help you in the best possible way.
As you showed that the word "author" in line 10 was used as a proper noun, we can consider that the same word in line 4 was used in a general way and did not specify an exact person. This is because proper nouns are terms used to specify something or someone, as the question states that the word "author" was not used with the same meaning in line 4, we can consider that this is the difference.
the Texans had religious motives to annex themselves. The Mexicans had forced the American immigrants to convert to Roman Catholicism, effectively revoking the freedom they held in the United States.
