Seeing a difference in web detection results is to be expected due to how dynamic the open web is. The indexes Google uses for web results are constantly churning based on a large number of factors such as page ranking changes. Since the Vision API WEB_DETECTION relies on Google's own indexes, it is therefore also subjected to this dynamic churn.
Requests may also be served by different Google frontends and in turn different Google data centers depending on the location of the request. Therefore some requests may be served by different versions of the web detections service as it is common for updates to take time to propagate across data centers.
Lastly, if you are using a different version of the Vision API it may be using a different model for label detections. The
Cloud Vision Demo uses the
V1 API for its requests, and keeps the default model setting of "
builtin/stable".