I have never heard this. Amount credited varies from jurisdiction to jurisdiction. You can contact the court clerk to find out the exact amount you owe, and the daily amount credited by the jail. You may also consider talking with the prosecutor to negotiate a lesser fine. An attorney might be able to get both citations resolved.
I have never heard of this. It is not that way in Harris County. Contact the county clerk and / or the sheriff to determine the amount of credit given for each day in custody.