If I understand correctly, ETF and index fund are orthogonal terms. An ETF is traded on the stock market -- in contrast to a mutual fund which you have to buy through other channels.

An index fund tracks an index rather than being actively managed.

I don't know about VSGAX specifically, but it could be both an ETF and an index fund.

It's an index mutual fund[1] that is also available as an ETF[2].

1: https://personal.vanguard.com/us/funds/snapshot?FundId=5861&...

2: https://personal.vanguard.com/us/funds/snapshot?FundId=0938&...

Index fund, it isn't trading in an exchange.