I think the approach is very much similar to the one you are used to for UK law firms. The only difference I personally noticed, and which i appreciated, was that I felt more comfortable talking about personal anecdotes that could explain why I was interested in commercial law in the first place. I think that US firms seem to be more open in reading people's journeys that brought them to where they are, and not too focused on how much you know about a particular area of law or business (even though you still have to be ready to answer technical questions nonetheless!).
So I would just recommend to be yourself throughout the process, either in your cover letter/application answers. Be genuine when it comes to answering the questions and really express your reasonings and intentions behind your choices and background.
Something I would stress though is do your thorough research and try to know as much as you can about the firm, even things that people might not know. This will work wonderfully for you. For instance, for my
Gibson Dunn vacation scheme interview I watched a video on youtube (which was not on the official page of the firm not it was advertised to be a video about
Gibson Dunn) I think it was a law event online where some trainees from the firm were talking about their experiences. One of them mentioned something she was able to do with the firm and I used that as a reason why I was very interested in the firm, and I remember graduate recruitment being very surprised cause nobody ever knew or mentioned that before. So, I would stress to be thorough when it comes to researching the firms you are interested in!
Good luck with the applications!
