Both warrants are due to failure to appear in court.
I was charged with animal abuse for the first one (had my little dog in the car for awhile, poor thing I forgot about him, but he was fine), and the second disorderly conduct and refusing to obey an officer.
The answer is, it depends. If these are criminal cases, then there is a good chance you will be arrested. If they are just municipal citations, then you probably will not be arrested. You must also know the local procedure rules. Some counties only require you to appear in front of a judge and the warrant will be quashed. Other counties require you to be processed through the jail in order to clear the warrant. I would call a local legal help line and get some firm answers before you go to court.