Most likely, the ISP will use some form of (deep) packet inspection.
In the most simple case, the ISP will distinct browsing traffic from other traffic by looking at the destination TCP ports. Any traffic going to destination port 80 and 443 will be classified as browsing, all other traffic will be classified as downloading. It could even be that the ISP is deploying transparent HTTP(S) proxies and all browsing traffic is routed through those.
In a more advanced setup, protocol inspection will be used: the ISP's equipment will monitor all traffic streams and will recognise HTTP(S) traffic based on the HTTP headers. Billing is then done based on the classification.