Your employer may offer you the choice of resigning or being fired --- the choice you make can affect your career for the rest of your life. Future employers look at resignation and firing in a different light. In general, you want to resign rather than let an employer fire you, because a resignation lets you leave on your own accord.
When a company fires you, it generally does so for cause, such as if you've failed to live up to company standards. This isn't the same as being "laid off." When a company lays off workers, it usually does so because of reasons beyond its control, such as a bad economy. Employers typically look at a termination and "laid off" in the same light: They may wonder why a company didn't want to keep you on board.
Resigning means you voluntarily leave the company, even if the company gives you no other option. This is much more appealing to put on a resume than a firing or termination. Employers know that there are a number of reasons why an employee might resign, such as needing to relocate or wanting a career change. Also, resignations tend to be less stressful: You can plan out a resignation well in advance, which gives you time to look for a job and map out your finances during your downtime.
In general, if you resign, you can't receive unemployment insurance benefits because unemployment only covers unexpected job loss. However, states usually don't cover workers fired for cause, either. Laid-off workers tend to receive unemployment benefits because they can't control their situation. Whether you're fired or you resign, you probably won't receive anything other than pay for hours worked, extended health insurance coverage and anything in your employment contract, such as a severance package.
A future employer may ask about the resignation or termination when it looks at your job history and sees a gap in your timeline. Thus, you should never lie about your situation in case of a background check --- but you can still soften the impact. If you were fired, avoid including the job in your work history if you can, especially if the job doesn't relate to your next job. If you resign, mention the positives you gained from the job, as well as your resignation and your goals with your new company, suggests Anthony Balderrama of CareerBuilder.