(though if you are fired and and you say layed off, they will find out if they decide to check).
Not necessarily. Many larger companies only verify the job title and dates of employment per company policy (some only give title or dates, in these cases usually dates not title). It's a good idea to find out what your company verifies. For example, my employer only verifies the title and dates so I could get fired and no other employer would ever know unless I did something illegal that shows up on a criminal report. Smaller companies, franchise locations, and privately owned companies often verify anything. They're not as strict with their records especially if the inquiring party has a hand signed authorization release for a background check from the applicant which many do or can get (if you want a job and they ask for a release, you'll give them one).
Employers may ask for a job or personal reference who they may/may not call. Just pick good references, people you trust to give you a good recommendation. You'd be surprised how infrequently some companies do quality due diligence. Some don't even do background checks. They skim your resume/application. If you get an interview, they may judge you on completely unrelated criteria like a firm handshake or if you look like a troublemaker. I'm serious.
A company like Gamestop uses The Work Number for Everyone, an automated system that only verifies job title and dates of employment. Sometimes that system not entirely reliable (occasionally they'll get dates wrong depending on how a company keeps their records or if the company was acquired by another company or if an employee goes from a corporate owned location to a franchise location). If an employer insists on speaking to your supervisor or a coworker, pick a good reference. You might be able to pick just a friend who never worked at Gamestop as long as they can BS some answers. There's no way for the person doing the background check to know. Still, if you just got laid off and were a good employee, you're better off picking someone who knows what you did and knows you did a good job. Gamestop also has entirely awkward job titles like Game Advisor or Senior Game Advisor that don't mean anything to other employers. That works against applicants of new jobs because Human Resources or the hiring manager may take one look at those job titles and put their applications/resumes aside because Game Advisor doesn't mean anything to them (even if they're just the equivalent to Customer Service Representative or Team Member or the like).
Yes, I work in HR and mostly do background checks. It's not glamorous so I'm looking for a new job.