I may be wrong, but I think that the white veil is an indication that the nun is a novice, and with the final vows the dark veil is substituted/awarded.
The white veil may be a step past novice. It all depends. A girl from my parish went into the Franciscan Sisters of the Martyr St. George last year and when we saw her in the fall, she wasn’t wearing a veil yet. I don’t know that she was considered a novice at that point. It all depends on the order. The Carmelites I’ve seen have a lighter color for novices.