Some colors in bird feathers are under the control of a single gene. This gene can be of wild type only or have one or more recessive mutant variants which are usually yield to dominant wild type gene in expression. Other colors can be the polygenic by nature that means several genes take part in their inheritance.
Each cell of every bird contains a duplicate set of genes: one set of genes is obtained from the mother, the other one comes from the father. When the genes in this duplicate set are different, dominant wild type color will mask a recessive color. The dominant gene will always be expressed while the related recessive form of this gene will be expressed only if the organism has both genes in recessive variant. That is true for all genes located on autosomes, chromosomes that are similar in both males and females. But if the gene is located on sex-chromosomes Z or W, its inheritance will be significantly differs from common rule. The reason is that Z chromosomal genes have their counterparts only in male’s (ZZ), but not in female’s (ZW) set of sex chromosomes; and genes of W chromosome usually do not have their counterparts on Z chromosome at all.
Most color mutations can be classified in one of two categories: recessive autosomal or sex-linked. When a new mutation occurs, only the breeding data can determine in which category the case is.

Fawn plumage coloration of Shafttail Finches is a sex-linked trait marked as Z^fw. In such case, male has to have combination of two mutant genes of this variant (Z^fwZ^fw) to be expressed as fawn, while a single copy of the mutant gene in female (Z^fwW) will always detectable in her fawn coloration. At the same time male of visual wild type can carry hidden mutant gene, as the counterpart gene of wild type (Z⁺) in his genotype Z^fwZ⁺ is expressed dominantly. Four combinations possible in the breeding are shown in Tables 1-4. If a male is carrying the sex-linked mutation Z^fwZ⁺ and female  is normal Z⁺W, we will obtain in offspring only mutant females Z^fwW; the other birds will be normal males Z⁺Z⁺ or split to fawn Z^fwZ⁺ and normal females Z⁺W, Table 1. With a male Z^fwZ⁺ carrying sex-linked mutation and a mutant female Z^fwW, we will obtain both: fawn males Z^fwZ^fw and fawn females Z^fwW, and also normal males Z^fwZ⁺ who carry the mutation, as well as normal females Z⁺W, Table 2. If the parent male is a fawn Z^fwZ^fw and the parent female is a normal Z⁺W, all offspring males will be the normal split to fawn Z^fwZ⁺, and all offspring females will be fawn Z^fwW, Table 3. With a mutant male Z^fwZ^fw and a female of the same mutation Z^fwW we will obtain 100% mutant offspring of Z^fwZ^fw, and Z^fwW, Table 4.

Creamino plumage coloration, as well as a fawn, is sex-linked recessive trait. Birds that have this coloration carry ino mutation in a Z sex-chromosome that is usually referred to as “cream-ino". This mutation will visually appear in females because no counterpart gene is present to suppress it. Normal shafttail males Z⁺Z^ino are described as being split to ino, a.k.a. split to creamino. Again, if a male Z⁺Z^ino is in pair with the normal female, we will obtain only female mutants Z^inoW; the other birds will be normal males Z⁺Z⁺ and normal females Z⁺W or normal males split to creamino Z⁺Z^ino, Table 5. With a male split to ino mutation Z^inoZ⁺ and a creamino female Z^inoW we will obtain creamino males Z^inoZ^ino and creamino females Z^inoW, and also normal males carrying mutation Z^inoZ⁺, and normal females Z⁺W, Table 6. With a creamino parent male Z^inoZ^ino and a normal parent female Z⁺W, all offspring males will be normal split to creamino Z^inoZ⁺, and all offspring females will be creamino Z^inoW, Table 7. With a creamino male Z^inoZ^ino and the same mutant female Z^inoW, we will obtain 100% creamino offspring Table 8.

These percentages refer only to hypothetical indications. The results of real pairings can be very different from these percentages by probability theory, but the result of an infinite number of pairings will.

Isabelle plumage color mutation of Shafttail Finches is a recessive autosomal, non-sex-linked, hereditary characteristic referred as A^ib. Such a characteristic is inherited by gene pairs. Each bird has two copies of every gene on autosomal chromosomes, one from each parent. If an autosomal genetic trait is recessive, a bird needs to inherit two copies of the gene for the trait to be visible, A^ibA^ib. If both parents are carriers, split to isabelle A^ibA⁺, there is a 25% chance with each chick to show the recessive trait A^ibA^ib, Table 9. If one parent is isabelle mutant A^ibA^ib, the second normal parent obviously doesn’t carry mutation and identified as AA, and all offspring are normal AA or A^ibA⁺, Table 10. If one of parents (in this case it doesn't matter male or female) is isabelle A^ibA^ib and the second one is normal split to isabelle A^ibA⁺, 50% of offspring will be isabelle A^ibA^ib, and the other 50% will be normal with a hidden isabelle mutation A^ibA⁺, Table 11. With both parents being mutants, we will obtain 100% of the offspring being isabelle birds, A^ibA^ib, Table 12.

In these tables the first parent's genetic contribution (gametes) across the top and the second parent's down the left side.

Albino  Shafttail Finches, I believe, are the result of combining two recessive genes: sex-linked ino, Z^ino, and autosomal recesive isabelle, A^ib. It means to get albino offspring both parents need to be carrying at least one copy of the ino and isabelle genes.                                                                                                                                                                                                               If both parents carry an isabelle gene (A^ib) and only one parent carry ino gene (Z^ino) some of their females offspring will be albino, Table 13.                                                                                                                                                                                         If both parents carry an isabelle gene (A^ib) and ino gene (Z^ino) some females and some males offspring will have albino coloration, Table 14.                                                                                                                                                                                                  Because albinism of shafttail finches require the coincidence of two different mutations, which makes a combined event of low probability, albino shafttails are extremly rare in aviculture.