Symplesiomorphy

Turning back to the development of pterosaurs to modern birds:

It is believed that dinosaurs and pterosaurs were Ornithodirans.
The dinosaurs went their way on the land and the pterosaurs went their way in the air.

Ornithodira --> Dinosaurs
Ornithodira --> Pterosaurs --> Primitive birds --> Modern birds

The similarities of dinosaurs and primitive birds are symplesiomorphic.
To visualize the idea I am expressing you can think of it this way:
Very early on there was a split of creatures into one line that became land-based dinosaurs and another line that became air-based pterosaurs. Over time, each line developed to adapt to their ecological niche.
The pterosaurs developed through a series of steps to primitive birds (basal paraves) and eventually modern birds.
The dinosaurs on the land developed at the same time on their own line, but eventually died off.
Similarities between dinosaurs and primitive birds are due to their common origin as ornithodirans.
Those similarities are symplesiomorphic.

The ancestor of ducks, geese and swans

http://en.wikipedia.org/wiki/Presbyornithidae

Presbyornithidae were a family of waterbirds with an apparently global distribution that lived until the Earliest Oligocene, but are now extinct. Initially, they were believed to present a mix of characters shown by waterbirds, shorebirds and flamingos and were used to argue for an evolutionary relationship between these groups (Feduccia 1976), but they are now generally accepted to be "wading ducks", the sister taxon [actually ancestor] of the Anatidae, and thus essentially modern waterbirds. They were generally long-legged, long-necked birds, standing around one meter high, with the body of a duck, feet similar to a wader but webbed, and a flat duck-like bill adapted for filter feeding. Apparently, at least some species were very social birds that lived in large flocks and nested in colonies.

Analyzing the three major branches

Working with the idea that very early on, three major branches of birds formed (water birds, shorebirds, and land birds), we can look at the landbirds.
As we have seen the chart shows them as green.
http://www.owlpages.info/downloads/A_Phylogenomic_Study_of_Birds_Reveals_Their_Evolutionary_History.pdf
But we can also see that the birds in brown are a subgroup of the landbird major branch.
So we see landbird subgroups in green and others in brown.
Turning to the birds in red, we note that they are in two distinct groups labeled Anseriformes and Galliformes. The Anseriformes are clearly waterbirds and the Galliformes are secondarily weak-flying landbirds.
Also, including the purple group, we see that they are secondarily flightless landbirds. So we can add them to the summary:

landbirds - green, brown, red (Galliformes), purple (Ratites)
shorebirds - gold (Charadriiformes/Charadrii)
waterbirds - blue, gold (Charadriiformes/Lari), red (Anseriformes)

All that is left are the grey and black groups, which as we have seen are still unsettled. So their lineages are unclear, but in time may become clearer. .
Everything we have seen, that is clear, supports the idea of a very early divergence into the three major branches, with subbranches stemming from each major branch.

Confirmation

http://www.owlpages.info/downloads/A_Phylogenomic_Study_of_Birds_Reveals_Their_Evolutionary_History.pdf

Quote:

Modern birds occupy a wide diversity of niches and exhibit a variety of behaviors. The broad structure of our phylogeny suggested diversification along general ecological divisions, such as water birds, shorebirds, and land birds.

By "diversification" I take it they are referring to ancestry.
As I have said, the ancestry of birds was into a few major branches with subbranches off those major branches.
The authors of this study confirm this, presenting the major branches as "water birds, shorebirds, and land birds".

 And the authors confirm the subbranching when they say:

Quote:

adaptations to these environments clearly arose multiple times,

They are confirming exactly what I have proposed.