Lokua, the terms used for discussing genetics for all plants and animals are the same, but that doesn't mean everyone understands them and uses them correctly. Steve mentioned that BP breeders have basically lumped co-dom and incomplete dominance together. To be honest, I don't understand the difference between co-dom and incomplete dom enough to be sure if this is true or not, but it gives an example of how in some circumstances some people might use terms incorrectly as long as it works good enough for their purposes.

I think I see where some of your confusion is coming from and I'll try to clarify some of it for you.

Heterozygous and homozygous refer to genes that a certain individual has. Specifically, heterozygous means the individual has 2 different genes at a certain locus, and homozygous means it has 2 genes that are the same. It has nothing to do with the parents, although that is often a really good way to figure out what genes an individual has. However, as you already pointed out in this thread, while extremely rare, it is possible for the freak mutation to occur. In practice, that occurs so rarely that it is safe to assume an individual carries the genes one would expect it to have received from its parents, so it is talked about that way a lot. Of course we don't always know exactly which genes a parent has or which one got passed on, but more on that later. For the rest of this post, I'm going to be assuming that no mutations occur. But even though I'll be talking that way, the fact is that the actual meaning of the words heterozygous and homozygous has nothing to do with the mother or the father or the pairing or any of that.

They also do not mean if a trait is visible or not. However, as long as you know whether the trait in question is recessive, dominant, or co-dominant, you will know what the visual appearance of the snake will be based on knowing if it is het or homo. A recessive trait will only be visible if the individual is homozygous for that trait. So in practice, saying a BP is homozygous for albino also means that snake is a visible albino, and saying a BP is het for albino also means that snake is not a visible albino. And a dominant trait will be visible if the individual is het and also if it is homozygous. A co-dom trait will be visible in both cases, but with a different appearance for het and homo.

In the example you gave, the mother was albino (visible albino, which means homo), the father was not. Unless you know whether the father is het for albino, you can't be sure of the genetics of the offspring. I'll start off assuming the father does not carry the albino gene (this would be homo normal). In this case, you are correct that the offspring would be het for albino, but I think the reasoning you used to get there was wrong, and sometimes having the right answer for the wrong reason can be the worst thing because it makes you think your reasoning was correct and leads to more confusion down the road. You are also right that this doesn't state whether the hatchling will be visible albino. What states that is the knowledge that the albino gene is recessive so it will never be visible unless the individual is homo for it. But again, in practice, it gets cumbersome to say "and since we know albino is recessive" all the time so that phrase gets left out when people talk about breeding an albino to a normal and getting het but not visual offspring.

You say the child could receive either, I believe meaning either the albino gene or the normal gene. This is incorrect. In this example, the child will receive BOTH. The mother has 2 albino genes, and she will pass on one to each of her offspring. The father has 2 normal genes, and he will pass on one to each of his offspring. So the offspring will have one of each, which is what het means, 2 different genes.

If you meant the child could either be a visible albino, or not visible, that is also incorrect, but for a different reason. Albino is a recessive gene, which means it will always be visible when the individual is homo albino, and will never be visible when the individual is het for albino. If we go back and change the example to an albino mother, and instead of a homo normal father we use a het for albino as the father, then you don't know if an individual offspring will be visible or not. The father has 2 different genes, and he will pass on one to each of his offspring, but you don't know which one will end up in which egg. You can expect to get roughly 50% visible albinos and 50% visible normals which are het for albino. You know you won't get any normals that don't carry the albino gene at all because the mother has to pass on one gene, and both of hers are albino. The odds rarely work out exactly, and it is possible even when you "expect" to get 50/50, to get all of one or all of the other.

You said pairing a het with a het confuses you because they are the same and so that should be homo. Well, sort of. Homo is a prefix that means "the same". Homozygous is a word that means an individual has 2 of the same genes at a certain locus. Two individuals can't be homozygous to each other even though they can be the same as each other. The words homozygous and heterozygous only talk about genes in an individual. The words mean nothing about the parents or offspring or anything you might pair up with that individual to breed. However, you can use the information to make a lot of conclusions about the parents, offspring, and what you'd like to breed with the individual to get the offspring you want.

You say you understand dominant and recessive, but also call them visible and underlying, which tells me you probably don't understand them. This is actually a common misunderstanding. Dominant does not mean visible, nor does it mean the gene is more likely to get passed on to the offspring (another common misunderstanding). Dominant means that the gene will be expressed (visible) if it is present in the individual, regardless of whether the individual carries 1 copy (het) or 2 copies of it (homo). Recessive means that the gene will only be expressed (visible) if the individual carries 2 copies of it (homo). This does mean that a dominant trait will always be visible in an individual that carries that gene at all, and a recessive trait has a chance of being underlying in an individual that does not show that trait.

You talk about getting an albino from parents that are both non-albino, and so they'd need to both have the recessive trait for albino. You also said that 1/4 of the offspring would be albino. This actually shows more understanding of how genetics and punnett squares work than a lot of people have, so it is possible that part of what you say that seems like you don't understand is just that you have worded things awkwardly. However, in the same sentence, you say that those offspring will have the dominant trait albino, which is wrong. They will have the visual trait albino, but that doesn't make it dominant. In BPs, albino is recessive. Always. Even when it is visual it is not dominant. It is just that when it is visual, that means both genes at that locus are the albino gene, so there is no room left for a dominant gene, so the recessive one becomes visible.

Phenotype does mean the visible trait an individual shows. Thus, "normal" is the phenotype of both a BP that carries 2 wild type genes, as well as one that is het for albino.

Genotype is what genes an individual actually carries, regardless of whether or not they are visible. so the 2 BPs above have the same phenotype "normal", but different genotypes with one being homo normal and the other being het for albino.

Well, this got really long but I hope it does help clear things up for you.