Factors and facets
In personality trait research, traits are often conceptualised hierarchically. There is also a broad consensus that a small number of broad traits (typically the Big 5, but others argue for different numbers such as the HEXACO 6) explain personality quite well. The big 5 also goes by the name Five Factor Model. The terminology of "factor" is quite likely linked to the method of factor analysis often used for scale construction in this area.
Several popular personality tests measure traits at two-levels (e.g., NEO-PI-R, HEXACO-PI-R, IPIP, etc.). So for example, the NEO-PI-R is composed of five broad factors, each of which is composed of 6 narrower facets.
So in summary, there is a range of terminology that have similar meaning:
- broad traits, domains, factors
- narrow traits, facets
Another common terminology is that of scales and subscales.
On basic level, this is just convenient terminology for describing two levels of a hierarchy of measurement, particularly where the broader level is defined by the lower level.
For further discussion see:
Anglim, J., & Grant, S. L. (2014). Incremental criterion prediction of personality facets over factors: Obtaining unbiased estimates and confidence intervals. Journal of Research in Personality, 53, 148-157. https://osf.io/g8kbj/
Your case of mapping a test onto a theory
In your case, you are mapping eight scales onto a theory that includes eight components. This doesn't have too much to do with the factor-facet distinction.
Perhaps the main issue is whether there is an overall scale (e.g., an overall leadership effectiveness scale, of which there are eight subscales). You could potentially call this the leadership effectiveness factor and call the eight elements "facets". But it might be more common to merely call the eight components "scales" or "subscales".