Mark, what you need to do is find the breakdown of the holdings within the relevant funds. The UK Vanguard links you posted include top 10 holdings info and see which matches the breakdown of the VTSAX best.
Vanguard Total Stock Market Index Fund is a 'whole US index', while Global Equity fund is 'whole world'.
So the quick answer to your question is that the US fund you posted is closer to VTSAX than the Global fund.
But, you are a new poster, I'll try to ask this politely - are you asking the right question? Why do you want to invest in US when you are in the UK? This is going to expose you to currency risk. Do you have UK holdings too? Are you clear on why the advice to invest in VTSAX is right for a reader in the US but might not be right for a reader in the UK?
Come over to the
UK Tax board - we cheat and have non-tax threads there too. The people there might be able to help more.
Cross posted with cerat0n1a :-)