Balance is the money sitting in your account between trades. Equity is balance plus or minus the current P&L of all open positions. If your balance is $10,000 and you are up $300 on an open trade, your equity is $10,300. Close the trade and the $300 moves from equity to balance.
Equity — not balance — is what margin calls and stop-outs are calculated against. A sudden drop in equity from an adverse market move can trigger a margin call even if the balance looks healthy.