Is ghusl required if there are daily white spots on the underwear, without nocturnal emission?

No, الاحتلام (wet dream) is the emission of semen during sleep. Ghusl (ritual purification bath) becomes obligatory upon seeing semen after waking up, even if the sleeper did not feel its emission. There is no disagreement among scholars on this point. However, if you find a white spot and are not certain whether it is semen or not, you can consider it semen and perform ghusl, or not, in which case you do not need to perform ghusl. This is the detailed ruling according to the Shafi'i school, which is the relied-upon opinion.