Is it obligatory to distinguish between sadaqah and zakat money?

Yes, this is obligatory because there are differences between sadaqah [voluntary charity] and zakat including the different channels for their distribution.

The circle of the recipients of sadaqah is wider than that of zakat. Zakat is distributed exclusively among Muslims based on the hadith of Abbas (may God be pleased with them both) who narrated that the Prophet (peace and blessings be upon him) said: "Zakat is to be taken from the rich among the Muslims and returned to their poor" [recorded by Bukhari and Muslim]. Moreover, it is paid exclusively to the eight recipients mentioned in the Quran: “Zakat expenditures are only for the poor and for the needy and for those employed to collect [zakah] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler - an obligation [imposed] by Allah. And Allah is Knowing and Wise” [9: 60]. This means that the recipients of sadaqah may include the eight channels mentioned in the above verse as well as others who may be either Muslims or non-Muslims.

The construction of mosques and service complexes for instance must be financed from sadaqah and not from zakat funds, since zakat is primarily spent on people and not buildings, for [deserving] worshippers and not for mosques. This is because the basic principle of zakat is to fulfill the needs of the poor and those in need and to maintain their livelihood as the Prophet (peace and blessings be upon him) made specific reference to them in the aforementioned hadith. The majority of scholars stipulated that zakat must be transferred to the possession of the poor, enabling them to spend it on their needs of which they are more knowledgeable. This aim cannot be achieved if the funds are spent on the construction of mosques or service complexes.
And God the Almighty knows best.