First, their similarities: In both counting and chanting, repetition
or re-application of a function leads to the presentation of a new
element. The new element can be one element in a series or string of
elements. However, while in a count this element is distinguished, in
a mantra it is not distinguished. Thus re-applying a function in a
count takes us from 4 (say) to 5; while a revocalization in a mantra
takes us from one sound (or image) to the next similar sound. While
the count and a mantra are both strings of signs, the mantra string is
neither countable, ordered nor repeated, nor are its elements
identifiable.
An interesting conclusion can be squeezed out of this.
A count has internal properties that give the conditions for its
presentation. These conditions are the human conditions of conferring
order. In a mantra, these human conditions are eliminated or bypassed.
They are by-passed by applying (e.g. vocalizing) a string of similar
members, thus reducing and eliminating the framework that supports
distinguishment, such as supports a count. Once the application of a
mantra eliminates the framework for distinguishing order, the objects
subsisting in that order also disappear. With the disappearance of
objects and their framework, internal properties manifest.
A caveat: In a count where the function applied is + 0, the repetition
of similar elements may or may not lead to a mantra string, depending
on the presence or absence of the framework or enabling (human
ability) condition of 'order'.