Some forms of HFT work by getting information from other exchanges before you, then front-running on price differences.

Front-running usually refers to a fairly specific scenario in which a brokerage or fiduciary executes orders as principal prior to dealing on behalf of their client so as to benefit from a market movement they anticipate will be caused by the client's orders.

This is categorically not what HFT firms are doing.

That's not what front-running is.

This is arbitrage, not front running. Front running requires not-public information.