Just as a perspective from another field (programming), censoring and truncating are two distinct operations.
When working with a sensitive dataset, for example social security numbers and telephone numbers, I might censor it or have it censored prior to access being granted:
123-12-1234 => 999-99-9999
567-56-5678 => 999-99-9999
(906) 123-4567 => (000) 000-0000
This allows the rest of the application to operate as it normally would, with similar data structures, but with no real informational content or dissemination of private information.
Truncation, by contrast, is typically just cutting off remaining values after a certain point. To work on an application, I don't need hundreds of thousands of records, perhaps I only need ~50 of each which makes the data access much faster and the data sets smaller.
A similar variant of truncation is when inserting a value into a column or datatype of limited length or precision:
abcdefghijklmnopqrstuv => abcdef
10.23412421345 => 10.23
10.92455311 => 10