Thank you for all your replies.
The thing about having different accounts was only to illustrate the point.
My situation is that I am setting up an account with truewealth, a robo-advisor similar to betterment (so I have read; I don't know betterment that well though).
In my account at truewealth I can choose how to allocate my invesments, say 50% bonds and 50% equities. Then according to my setup, they buy shares of an ETF that reflects that allocation (so they buy 50% shares of 1 bond ETF and 50% shares of 1 equities ETF). I just wanted to check that this way my portfolio is actually diversified, and not that I need to have the 2 ETFs somehow connected to be actually diversified.
This also means that if I want to have a "total market equities", I can buy ETFs covering europe, USA and emerging markets, I would have a "total equities market"?
I ask this because truewealth has main categories (e.g. equities, bonds, REIT, ecc) and sub-categories, which are basically countries (switzerland, UK, USA, europe, emerging markets). So if I mix a little bit of everything (say 25% switzerland, 15% uk, 25% usa, 25% europe, 10% emerging), meaning I have 1 ETF for each of the sub-categories, I do have a "total equiities market". [I might have forgotten asia here, but it's just for the sake of understanding]
p.s. I know just setting up a vanguard fund would be much easier, but I want to invest a small initial sum applying DCA, and even after that I want to invest smaller sums each month (and still apply DCA).
p.p.s Why DCA? Because it's my first investment and I know I couldn't bear to invest and see it go straight down; I know that in the long term limp sum investing is better, but I don't know how long term it can be, and as I said it's a psychological thing.
Thaks