I got an offer for a job that requires a moderate risk public trust and there are some discrepancies between my resume and and my experience that I would be putting down on the form. One of the job titles I changed to reflect my job duties more and also I added 8 more months on that job and also I added one year onto another job in the past and three months on to another job. I did work at those places and I did do the work that I listed on my resume, but I added time because I wanted to shorten my resume. There are jobs in between that covered for that added time and they reflect experience in relation to the job that I’ll be receiving. Will this be a problem when they do the investigation? Should I list my work history with the jobs that weren’t on my resume? Are they comparing my resume to the SF85P?
Carefully read the instructions on your SF85. It doesn’t matter if you worked there for one hour or one decade. If you worked there in the last 7 years, it needs to listed with correct dates. Some agencies require resume review and some don’t. Regardless, the SF85 needs to be completely correctly.
Follow the instructions exactly. Gov applications (sf85/86) require you to account for every second of your life during the scope of time (7-10 years). You have to list all periods of employment AND unemployment (including study time).
To add to the other replies already given, if the agency orders a resume review then the investigator will be given a copy of your resume and they will go through it line by line and ask about every discrepancy and you will have to provide the correct information and the reason the information on the resume is not correct.
I got chewed out by my BI for providing my nickname for my middle name. I’ve always used that and it didn’t occur to me to use what was on my birth certificate. It ended up fine though 
A nickname should be listed on the SF86 under other names used. On the resume you could always say, for example, John (Jay) Doe. That way your legal name is on there as well as the name you go by.