"Fired" generally means terminated for cause, though not exclusively so. "Laid off" implies a general workforce reduction, and maybe some severance payment, job placement help, etc.

Either way you're out of a job, so in that sense there's not much difference.

Depending on the country/state laid off and fired be very different legally.

Laid off generally comes with a severance package that is consistent across the laid-off employees. The reason for the employee termination is (at least outwardly) the companies fault due to the company not having a use for that subset of employees - department closure, cashflow, product cancellation etc. In the UK a company must announce it is going to go through a lay-off some weeks before actually terminating employment contracts.

Firing someone puts the 'blame' on the employee. Generally the company has to document the reason for firing the employee. Even in places with 'at will' employment law a company will want documentation in place in order to defend against wrongful termination or discrimination claims.

Companies will often offer some cash sweetener to a fired employee in return for them signing a termination contract that makes future legal claims more difficult (or costly).