There is no difference. 'Attending an ASC' means 'attending your biometrics appointment at an ASC'.
There are 2 types of places where you can give biometrics:
1. A USCIS Application Support Center (ASC), which is free of charge and is run by US immigration on behalf of UKVI. This is where the majority of people give biometrics. You can book biometrics at any open USCIS ASC in the US (there are 129 of them. You can find your nearest one here:
https://egov.uscis.gov/office-locator/#/asc). Once you have attended biometrics here, you mail your passport to New York City for visa processing (and you upload all your documents to the VFS Global website).
2. One of the 10 VFS Premium Centres in major US cities (Atlanta, Boston, Chicago, Houston, Los Angeles, Miami, New York City, San Francisco, Seattle, and Washington DC). It costs either $1,200 (standard service) or $2,000 (premium service) on top of your £1,523 visa fee and £1,872 IHS surcharge. You cannot book biometrics here unless you are paying for either the $1,200 or $2,000 service. These services include document checking, scanning of your documents, and you get to keep your passport while the visa is processing. The $2,000 service also includes the $800 Settlement Priority processing (hence why it cost $800 more).
Basically, option 2 (VFS Premium Centre) is a complete waste of money and doesn't get the visa processed any faster than just attending an ASC and purchasing the $800 Priority Processing... you're essentially just paying the extra $1,200 to be able keep your passport while the visa is processing.
