tweet_volume is a value that relates to the Ads API and is not currently documented for general use cases. It can be disregarded if you are retrieving results successfully.
I’ve no idea how that site derives its results. I would imagine that they might be listening on the Streaming API and making up their own results, it is not clear. If it does not match the results from the /1.1/trends/place.json endpoint, I can’t really comment on the reason, sorry.