Is there is difference between "homozygosity" and "homozygosis"?
Homozygosis and homozygosity are NOT synonymous. The two terms refer to the same concept though.

Homozygote

An indivdidual or a cell is said to be homozygote for a particular gene (or any DNA sequence) when identical alleles of the gene are present on both homologous chromosomes. (Wikipedia > Zygosity).

Homozygosis

Homozygosis is the state of being homozygote (Wright 1933) for a particular gene (or any DNA sequence). According to freedictionary.com, homozygosis may also refer to the process of formation of a homozygote. I have never encountered this sense in the literature though. As you found out by yourself, Homozygosis is a term that is rarely used in the literature (in comparison to homozygote and homozygosity)



Expected Homozygosity

Expected Homozygosity is the probability of two randomly sampled alleles (in a population and at a given locus) to be identical by descent.

Expected homozygosity and Expected heterozygosity

As shown in Nei 1973, the mathematical expression of expected homozygosity $Ho$ is

$$Ho = \sum_{a=1}^{n} x_a^2$$

where $n$ is the number of alleles and $x_a$ is the frequency of the allele $a$.

It is more common to use the concept of expected heterozygosity $He$ (a.k.a. gene diversity) rather than the one of expected homozygosity $Ho$. By definition, $He=1-Ho$, that is

$$He =1- \sum_{a=1}^{n} x_a^2$$

In the special case of a bi-allelic locus, and replacing the two allele frequencies $x=1$ and $x=2$ by $p$ and $q=1-p$, the above formulations becomes

$$Ho = p^2 + q^2$$
$$He = 1 - (p^2 + q^2) = 2pq$$

Hardy-Weinberg equilibrium

Under the Hardy-Weinberg assumptions, the observed frequency of heterozygote (a.k.a. observed heterozygosity) is equal to the expected heterozygosity and observed frequency of homozygotes (a.k.a. observed homozygosity) is equal to the expected homozygosity.