While the numbers on the Enneagram symbol or diagram as used by Gurdjieff and the Fourth Way represent a sequential process as it moves clockwise around the circle, with the personality types the Enneagram numbers don't represent any such movement.
The only purpose the numbers themselves have besides being a label is to position the types around the circle. The circle and other elements of the symbol are then used to explore relationships between the types.
Labeling yourself as a number
What can sound a little strange when first encountering people describing themselves or others as an Enneagram type is how they refer to themselves or others as numbers.
For example, someone might say "I'm a type 1" if the type 1 personality is the best fit or "she's a type 2" if that type best fits for her.
Generally, a person identifies which of the types best describes their personality. They then use that number as a label to indicate which type is the best fit for them.
The numbers are neutral and consistent in that they don't attempt to describe the type through any particular interpretation.
Using a word label instead
Word labels are also given to the types by a number of authors and teachers. The caveat is, unlike the number labels, different authors and teachers may use different word labels for the types.
For example, one school of the Enneagram types may refer to type 1 as the Perfectionist, while another as the Reformer, and another as the Good Person, etc. All the schools agree on the label of Type 1 but don't agree on what word label to use.
The word labels tend to emphasize only one potential aspect of a type. If someone relies too much on the word label then they risk a very limited and sometimes stereotypical understanding of the type.
Someone might say for instance, "I must be a type 1 because I'm a perfectionist" when the reality is that people of different types can be perfectionistic. You may also hear something like "she can't be a type 2 because she's not a helper" when helping may or may not be how type 2 gets expressed through personality for a particular individual.
Differing interpretations of the types
While using the numbers to refer to the types is more neutral with everyone agreeing on the numbers, it belies a difference of understanding underneath the surface.
There are as many interpretations of the types as there are people teaching and learning about the types. Sometimes it's simply a matter of subtle differences between the schools and what they consider most important about a given type. Other times it's more about someone new to the types not really having a good understanding of them.
On the surface, when two people are describing someone as type 1 for example, it may first appear that they're talking about the same thing. However, when you dig a little into each person's interpretation of type 1, you'll likely begin to see some differences.
So while using the numbers seems to be the best way to refer to the types, the deeper conversation to be had is how each person defines and understands each type. You may find that people are using the same label to refer to different things.