A fixed asset is a long-term asset that provides your business economic benefits over its useful life (more than one year).
Expenses are one-off items or services that provide economic benefits only up to the point they are consumed.
For example, a car is an asset that can be used over many years. But the fuel you put in the car is an expense as it can only be consumed once.
Expenses appear in the P&L directly, whereas assets are put on balance sheet and then amortized (intangible) or depreciated (tangible) over their useful life.