@Andrei Radu How would you go about explaining an interest in private equity firms at the interview stage if you don't have any direct experience? would just highlighting some similarities between other experiences and PE be fine?
I think it would be and you definitely are not expected to have any direct experience working in the PE industry. Getting PE roles is notoriously difficult even for the people that have spent some time in IB roles at top bulge bracket banks like Goldman Sachs and JP Morgan. Getting internships at PE firms straight out of university is another level of competition - one can only realistically succeed if they are already commited to working in finance rather than law.
The way I used to go about justifying an interest in PE was by starting out with an interest in M&A. I would explain how working on transactions involving the selling and buying of companies is interesting to me because I liked learning all there is to know about different businesses and the industries they operate in; and how I enjoyed the process of negotiating deal terms (here, making a link to a negotiations competitions example or Forage Experience).
Finally, I would differentiate between M&A work done for corporate clients and PE clients, focusing on one or two features that make PE work more attractive. Examples include more streamlined deal processes, because PE clients are very experienced and sophisticated, and a greater variation of industries and sectors involved, as PE clients do not have the same business parameters limiting investments as corporate clients do.