I think the choice to use the word "anejo" mostly has to do with whether or not the producing country is Spanish-speaking. Appleton V/X, for example, is classified by BarMedia as an anejo rum, but Appleton--from English-speaking Jamaica--doesn't use that term on the label.
As with Tequilas, the term seems to be applied to the older aged spirits, more than 8 years.
Style differences in rums seem most apparent when you sample the different language groups, i.e., Spanish, French and English.
So, if the question is, is there among long-aged rums a specific style that uses the term anejo, I have to say the answer is no. BarMedia, for example, uses the term generically to apply to any long-aged and, therefore, snifter-worthy rums, regardless of whether or not the word "anejo" appears on the label.