DUI and “drunk in public” are misdemeanor crimes in California designed to protect the suspect and the public from a suspect's dangerous, substance-induced behavior. Both laws criminalize a suspect's being intoxicated in certain settings. But the level of intoxication that must exist for each crime to take place differs significantly.
In short, DUI requires that the suspect's mental and physical faculties be impaired—at least to the extent that he can no longer operate a motor vehicle with the same skill and caution of a sober person. Whereas Penal Code 647f Drunk in Public requires that the suspect be extremely intoxicated—so much so that he can no longer safely care for himself or others, even while just walking around.
The DUI standard of intoxication remains somewhat nebulous and the subject of much debate—both scientific and political. California sets a per se BAC limit of .08 for drivers. But most experts agree that some people who are sensitive to alcohol can become impaired at a much lower level, in some cases as low as a .02 BAC. On the other hand, some individuals with a higher tolerance for alcohol can maintain sober-like faculties at a .10 BAC or higher.
In any case, one doesn't need to be drunk to fall within the purview of California's DUI laws. A low to moderate degree of intoxication can trigger and arrest and possible conviction. “Drunk driving” is therefore a misnomer. “Impaired driving” would better describe the standard.
Penal Code 647f, by contrast, is triggered only when the suspect is flat-out drunk. One could be well within the range of intoxication for DUI purposes, but well below the range for “drunk in public” purposes. This difference in standard makes sense. A person could create a hazard just by walking around in public sufficiently inebriated. But that hazard exists much sooner when the person combines alcohol and driving.