Oxford says: respect 3[C] a particular aspect or detail of sth: In this respect we are very fortunate. Ç There was one respect, however, in which they differed. aspect [C] a particular part or feature of a situation, an idea, a problem, etc.; a way in which it may be considered: The book aims to cover all aspects of city life. Ç the most important aspect
With regard to those two definitions from Oxford, think of respect as way; think of aspect as way of looking at something or way of considering something.
In this [respect / way] we are very fortunate. There was one [respect / way], however, in which they differed. The book aims to cover all [aspects of / ways of looking at / way of considering] cit