Melasma with Pityriasis Versicolor: This combination is a common cause of dark discoloration on the face, especially in areas exposed to the sun, coupled with white circular patches due to Pityriasis Versicolor, a fungal infection that can cause hypo-pigmented patches.

Vitiligo with Melanosis: Vitiligo can cause white patches due to loss of pigment-producing cells, and when combined with conditions that cause darkening of the skin (melanosis), it could present with both dark discoloration and white patches.
Pityriasis Alba: A mild form of eczema that can cause light patches on the face, often accompanied by mild darkening of the surrounding skin due to inflammation or post-inflammatory hyperpigmentation.
Post-Inflammatory Hyperpigmentation (PIH) with Tinea Faciei: PIH can cause dark spots after inflammation, and when combined with Tinea Faciei (a fungal infection of the face), it might present with both dark discoloration and circular patches.

Leprosy (Hansen's Disease): Although rare, leprosy can cause skin discoloration and patches, including light or dark spots, and is critical to diagnose early due to its potential for serious complications and the need for specific treatment.
Sarcoidosis: A condition that can cause skin lesions and patches, including those that might appear as dark discoloration with white circular patches, and is important to diagnose due to its systemic implications.

Idiopathic Guttate Hypomelanosis: A condition characterized by small, discrete, hypopigmented macules, which could be considered in the differential for white circular patches, though it's less likely to be associated with widespread dark discoloration.
Phyllodes Tumors with Skin Metastasis: Extremely rare, but in cases where there's an underlying malignancy like phyllodes tumors with skin metastasis, unusual skin presentations can occur, including pigmentation changes.