Does the Liquidation Process Differ between a Cross-Margin and an Isolated-Margin Position?

Yes, the process differs significantly. In an isolated-margin position, only the margin allocated to that specific trade is used, and only that position is liquidated.

In a cross-margin position, the exchange draws from the entire account balance to prevent liquidation. If the entire account equity falls below the maintenance margin, all cross-margin positions will be liquidated simultaneously.