The Matt Berens tree has pink blossoms
Perhaps you are speaking of the mimosa tree. It has delicate pink tendril like flowers and pole bean pods in the fall with seeds in them.
The Eastern Redbud (Cercis canadensis) is a deciduous tree that produces pale pink tassel-like flowers in spring. This tree is known for its showy display of flowers before its heart-shaped leaves emerge.
Cherry trees
It's an apple blossom tree.
In the Philippines, it is called Macopa. Its fruit is pink and bell-like. Other names are Bellfruit and Rose Apple.
One ornamental tree that starts with the letter "P" is the Pink Dogwood (Cornus florida). It is known for its beautiful pink flowers that bloom in spring.
The tree adorned with pink flowers and green leaves is likely a cherry blossom tree.
magnolia
It sounds like you are describing a silk floss tree (Ceiba speciosa). This tree has large thorns and produces vibrant pink flowers when in bloom. It is native to South America.
dogwood?
One common pink flowering tree is the cherry blossom tree. It is known for its beautiful pink blossoms that bloom in the spring.
A bushy low growing tree with white spring flowers