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Calico cats are cats that have 3 fur colors and are always female or males two X chromosomes.
I've seen many cats that will have 2 fur colors (one of them is usually white) and another, third, color which is a darker shade of one of the other colors. As exampled in the pictures below (taken from the internet). Are those considered Calico cats?
(source: mirror.co.uk)
I think you are misunderstanding "color" here. When applied to cats, it doesn't literally mean a color shade as used in color theory, but "coat color" which can in fact also be a "coat pattern".
The cats above are two-colored, not three-colored. One color is white. The other color is what is called "tabby" in English and is a pattern of dark spots arranged in regular stripes on a lighter background. These spots are not considered a third color in cats.
This is a calico cat. Her three coat colors are white, orange, and grey tabby. See how the orange and grey are irregularly interspersed, this is the pattern of paternal and maternal chromosome expression on her body. Again, the grey and black patches within the tabby part are regularly placed. They don't make two separate colors, grey and black, but a single coat coloring, grey tabby. There are also other color combinations in calico cats, for example white-orange-black, and they are more straightforward to recognize.
Tortoiseshell cats (which is the normal name for Calico style cats in Europe) arise due to a gene on the X chromosome. Some patches are ginger, and some tabby due to the deactivation of one X chromosome in each cell at an early stage of development. This produces a tortoiseshell-like pattern.
What you see in these tabby cats with the white colouring is due to temperature dependence, this gives the patterning on the feet/nose etc. Tortoiseshell cats looks quite different, where the different coloured patches of fur are random.
Adding to this massively late, but while the cats in the first pictures are "just" black tabbies with minor white spotting, the cat in the second picture may actually be a diluted caliby! A diluted caliby (calico-tabby) is a black, orange and white cat with a tabby gene and a double dilution gene! This makes them a blue, cream and white tabby, shortly known as caliby. Unless the light is playing tricks on me, you can see a cream-colored patch on her right cheek that indicates the presence of ginger/cream. As almost all cats that possess both a black and a ginger color are female, with only very rare exceptions, the second cat in this case would likely be female. Note that the color white is not a sex-linked color and does not indicate any gender! Important is the presence of both a black-based and a ginger-based color!
And a tiny crash course on the cats in the first picture: To tell the true color of a tabby cat, look at the stripes, especially at the tail tip. You can see their base color is clearly black, whereas the rest of their body has various shades of black due to the agouti gene, which gives each individual hair little stripes and creates the tabby pattern through that! If the cat is a torbie (tortoiseshell tabby, black + orange tabby) you will notice patches where the stripes are ginger instead of black.
