Its true in the broadest sense of the words, with regards to colour all budgies do fall into one category or another, but they are referred to as blue series birds or green (sometimes yellow) series birds.

There are only two basic colours in a budgies genetic make-up BLUE and YELLOW.  It is by the removal, or separation of these colours that other colour variations are possible.  It you think of it as a painters palette it might become clearer.  By mixing yellow with blue you get green, similarly in reverse if you take the yellow away from green, you're left with blue.

These two stars represent the colouring of a budgie.  If you remove the yellow pigment from the bird, you're left with...

....blue and white

An ordinary budgie has black trimming to the feathers, on some birds this trimming is a brown shade.  Sometimes dark, sometimes quite light, this is referred to as CINNAMON.

BLUE SERIES

Obviously all of the blue birds fall into the blue series category, but so do greys and whites! So now we have three different colour birds that are all "blues".  But it doesn't stop there, the actual blue birds come in different shades...

From left to right:    Sky Blue     /    Cobalt    /    Mauve    /    Violet

(It has been brought to my attention (& I concur) that the Mauve & Violet birds above are not good representations of these colours.  For some reason the camera does not reflect their true colours very well.  The pics above will be replaced as soon as suitable replacements can be found.  Keep your comments coming "Help me make this a better site for you!!!")

This picture clearly shows colour variation

All of these birds are classes as Sky Blue

The lightest of the blues is the Sky Blue.  Next and slightly darker is the Cobalt, followed by the mauve.  Darkest and most striking of all is the violet.

However, just to complicate things even more, some (quite a lot actually) birds are a shade `somewhere in between`.  In these cases use your own judgement as to whether it is a dark sky blue or a pale cobalt.

Similarly with the Greys, they come in a variety of shades (if there is names for them I don't know them).

Greys can be anything from pale nearly white at one end of the scale to so dark grey that they appear virtually black.

The method applied that results in the blue mutation can be taken a step further.  Take away all colour pigmentation, the blue and the black and you're left with just white - the Albino!  There are some other varieties that are also completely white, but Albinos can be easily identified by examination of the eyes.  Albinos have red eyes, any other variety will be black.

Blue birds do not carry the green gene, the yellow pigment is completely absent, and not dormant as some people believe.  So therefore, it is impossible to breed a green bird from blue parents.

YELLOW-FACED BLUES

As I have already said the yellow pigment is absent in blues, however, in these birds the yellow pigment is present but only to the extent that it shows in the face of the bird.  Some birds appear to have a yellow wash through their wings, this is quite common, as is the greenish appearance of the body of some (blue) birds.  They are still blue birds, and to refer back to my comparison of a painters palette, sometimes the colours aren't mixed very well and seem to run into the others, in this case the yellow into the blue.  All varieties can have the yellow-face gene but it is only visible in the blue, grey and white birds.  If a green series bird is a yellow-face then it is hidden amongst the natural yellow colouration and only breeding results will show that it is indeed a yellow-face.

From left to right: Yellow Face Sky Blue / Yellow Face Violet  / Yellow Face Cobalt / Yellow Face Grey

GREEN SERIES

Green birds can be split in five groups Light Green, Dark Green, Olive, Grey Green, and Lutino.  Sound simple? Well as with the blues, each of these varieties can be split into a variety of shades.

Light Green                        Grey Green                                Wild Budgie

                        Dark Green                        Grey Green                                                Olive

I've include the wild budgie for comparison.  As you can see the Greens as well as the Blues come in a variety of shades.  The two Grey Greens above demonstrate clearly how much these shades can range.  Incidentally you can get darker greens than those above, as can they be lighter.  Olives, which are quite rare (you're unlikely to ever see one) can be very similar to Grey Greens in appearance, so much alike in fact that at times they can only be distinguished by the colouration of their cheek patches.  Those on the Olive being Violet/Blue, whilst those on the Grey Green are grey.

The Lutino is to the Greens, what the Albino is to the Blues.  All overlaid colour pigmentation is removed, leaving the base colour, in this case yellow.  There are some other varieties that are also completely yellow, but Lutinos can be easily identified by examination of the eyes.  Lutinos have red eyes, any other variety will be black.

If one of the parents of a green is blue, then that bird will be carrying the blue gene, or on a more technical note split for blue.  All this actual means in reality is that if you pair this bird to another blue bird the chances of having blue offspring will be increased.  With regards to breeding, green is dominant to blue, but by using one bird that is split you can balance the scales a bit.  There are not visual attributes that will tell you a bird is split, it is only by examining breeding results that this can be determined.

MORE ABOUT GREY GREENS

Now that you're comfortable with Blues ands Greens I'll complicate the matter and tell you more about Grey Greens.  Firstly let me say that Grey Greens are Green Series birds.  However, they also carry visual blue attributes, namely the grey colour.  Grey is probably the most unusual colour in that it can be a colour by itself or it can blot out, or be overlaid onto another colour.  In this case the grey colouration is overlaid onto green, resulting in a unique blend of the two. 

From a pair of Grey Greens it is possible to breed the following colours...

                Grey Green        Green         Grey        Blue.

Whether these are Dark or Light in shade is dependant on how dark or light the parents may be.  It is worth pointing out that whilst it is possible to breed blues from grey green parents it is quite rare

CINNAMONS

Although they aren't a colour on their own, any of the colours mentioned above can be Cinnamons, they are still worth noting and looking at.  Take an ordinary budgie with the standard black trimmings to head and wings and replace these with brown and hey-presto you've got a Cinnamon.

For some reason Cinnamons are usually paler in colour than their black counterparts.

THE HALF SIDER

A half sider is a budgie that is colourwise split in two, part of the bird is blue and part is green.  as far as I know you cannot deliberately breed a half sider, they are a result of genes splitting and developing wrongly whilst still in the egg.  The amount of the colour split can vary greatly from a 50/50 split to a spot of the alternate colour somewhere on the body.