If they didn't take me to jail and just put handcuffs on me, is it still considered an arrest?

Recently I have been pulled over for a DUI. Officer gave me the field test and breathalyzer test. I did passed the field test but officer still told me to do the breathalyzer. I’ve had two beers at that night. I blew 0.07. He put the handcuffs on me and told me to sit on side. Then told me to call someone and wait until he picked me up. The police officer gave me a yellow color ticket and it showed a date and time to show up at court. 23152 (0)VC- DUI Misdemeanor(circled). They never took me to jail or took finger prints or anything like that. My license was never revoked either. I showed up at court on the court date and the clerk said 'there is no case has been filed on me'. They put a time stamp and told me to go. Then I talked to the DA's office and told them what happened. Then they sent me a letter something called "failure to file charges or dismissal" which shows which they didn't file the case. Few weeks later, I called the DMV about my records. They said I have an arrest record. I’m confused. Does it stay on my records for very long time? Please help. Thanks in advance.