The same position, two rules
Isolated margin assigns a fixed amount of collateral to the position. The liquidation sits close, and when it happens the loss is exactly that collateral — the rest of the balance is untouched.
Cross margin backs the position with your entire balance. The liquidation is far away, sometimes very far, and the position can consume everything before reaching it.
isolated: liquidation ≈ entry × (1 − 1/leverage + MMR)
cross: same formula with effective leverage = notional ÷ whole balance
A $5,000 balance holding 0.25 BTC at $60,000 is $15,000 of notional. Isolated at 10x liquidates about 9.5% away and risks $1,500. Cross treats it as 3x, liquidates roughly 32% away, and risks the full $5,000.
Neither is safer — they fail differently
This is the part usually stated as a ranking and it is not one.
Isolated bounds the loss and gets you liquidated more often. A normal retracement can close a position that would have recovered, and you lose the margin assigned. The failure mode is being right and stopped out anyway.
Cross gives the position room to survive noise and removes the ceiling on the loss. The failure mode is a position that keeps being given more rope until there is none left, and the loss arrives as the whole account rather than as a line item.
The choice is genuinely between bounded loss and survival room, and which you want depends on whether you trust the stop or the thesis.
The version that actually hurts people
Not choosing.
Cross is the default on several major exchanges. A trader who never opened the setting is in cross without having decided to be, sizing positions as though the loss were capped at the margin shown on the screen. The number displayed as "margin" in that mode is not a limit on anything; it is an accounting entry.
The first useful action is to open the position settings and read which mode is active. The calculator exists to make the difference concrete once you know.
If you use cross, the stop is not optional
Under isolated margin the liquidation acts as a crude backstop — expensive and ugly, but bounded.
Under cross there is no backstop at all until the account is gone. That makes an actual stop-loss order the only thing standing between a bad trade and the balance, and it makes position sizing more important rather than less: the position size calculator assumes the loss stops where you put it, which under cross is true only if you place the order.