For ease of explanation let me first tell you that the "genetic makeup" is called "genotype" and that "how we look physically and psychologically" is known as "phenotype". These are not complete definitions of the terms but this should help you understand what we're talking about. I also apologise for the lack of detail or inaccuracies which many fellow contributors may find aggravating, but the question calls for keeping things down to the most important aspects :)
Do genes define how we look?
Genotype defines to some extent the human phenotype, but we don't know exactly to what extent regarding most aspects of the phenotype. This is called the "nature vs. nurture" debate and is concerned with the effects of genotype itself on phenotype vs. the effects of non-genetic influences after fertilisation (such as chemical surroundings during embryonal growth, experiences at young age etc).
Numbers of genes from males and females
Another misunderstanding is that a sperm carries a certain number of genes which it combines with a number of genes from the egg. While this is strictly true, the number isn't what matters because we all carry the same number of genes (*). The genotype doesn't depend on the number of genes, but rather, almost all genes exist in several variants within the human population. So the genotype is actually about which variants an individual carries, not about the number of genes. In biology, we use the term "allele" to refer to variants in this context. So in other words, each gene can have different alleles.
People with identical appearance
If two people have identical alleles for all genes (i.e. identical genotype), then they can indeed look almost identical. However, because of the vast number of genes and alleles present in the human population, it is practically impossible for the same alleles to come together in two humans. With only one exception: if two individuals result from the same combination of sperm and egg cell, they will be identical, and this is exactly what happens in monozygotic twins.
Similarities by geographical region
However, the total number of genes and alleles is limited (**). This concept is what people call the "gene pool" and is the reason why humans are still always humans and share certain similarities. In particular, for most of human history our geographical movement has been limited (most of the time), creating geographical "sub-gene pools" (to keep it simple). This is why people from the same geographical region are more likely to look similar; they have a higher chance to share the same alleles of genes that determine appearance. In terms of behaviour - to whatever degree genotype influences behaviour, peopel from the same geographical region will be more likely to be similar in these regards than people from different geographical regions. However, you can now hopefully understand why this "degree of similarity" is next to impossible to quantify (lack of knowledge: which genes determine what, how many alleles exist of them, how many people have which allele, how much and how far do people travel,...).
(*) Ok, not quite - it is possible for an individual to have the odd gene actually completely missing, but for the sake of simplicity we all have the same number.
(**) Again, not strictly, because new alleles and possibly even entire genes can result from mutation, but this is relatively rare and on the large scale you can work on the assumption that they are limited in number.