The avast browser extension will essentially have a data base of suspects, etc., most likely actually coming form other sources (the antivirus side in the form of the Web Shield and other sources). It isn't scanning the website in real time, that is where the Web Shield comes in.
The Web Shield is a live scan the web site content and external links, some information/data of prior web shields scans may be included in the avast browser extension database.
If you download something from that site, pages to display in your browser and or files you seek to download, that will be scanned by the Web Shield and possibly also the File System Shield.
The avast browser extension, is for me not a patch on the live scans of the antivirus shields. Yes it may prevent you visiting a site the avast browser extension considers suspect.
Just have a look at the numbers items in the list of search and then just how many actually have a tag from the avast browser extension. I hope you are getting the idea that the avast browser extension isn't a replacement/patch on the Full Antivirus product.