Orthonormal Basis
An orthonormal basis is formed by two perpendicular unit vectors.
Standard Basis
The base formed by 
and 
is called the standard basis or canonical basis.
The standard basis is the most commonly used base and unless noted otherwise it should be working on this basis.
Orthonormal Basis in 3D
The three basis vectors are mutually perpendicular and also have a length of one.
The base formed by 
, 
and 
is called the standard basis or canonical basis.
