Question about loans against equity

So I'm trying to wrap my head around this whole equity thing, here's what I know;

1) Equity is the value of the house that you currently own, I get that.

2) You can get loans from the bank using your equity as security.



My knowledge gap;

1) When I am a first home buyer, I have no equity, no security, just my cashflow from my job, but I can secure a home loan, no drama.

2) When I DO have a home, and have equity, and I get a loan against it, how does the equity/security differ from just getting a loan with no security/property?



Example;

I own a $400,000 property outright.

I need $50,000.

I get a loan from the bank using 50K of equity.

I know own only 450K worth of my house, but I now have $50K to spend/invest



My question:

Do I still need to pay off that 50K loan? Or have I just traded part ownership of my house to the bank, for money/liquidity?



If I do need to pay them back, then that implies I have enough cashflow to service the loan, which then implies I wouldn't need to use equity as security because I can already service the loan without equity!!



I'm so confused by it. Do I need to pay off equity loans or not?

Question about loans against equity