News sentiment score tells us the overall sentiment of the whole news article, while keyword sentiment score shows only the sentiment score of the keyword through search.
The main difference is with or without keyword search involved. Without keyword search (e.g. in news pages), the sentiment scores are text or news sentiment scores that represent the sentiment of the text. With keyword search, the sentiment scores are keyword sentiment scores that represent the sentiment of the keyword only.
Please also see Q8, Q28, Q35