A 'top graduate school' is actually somewhere that probably gets a large number of applications from students (Stanford etc.)
That means when you apply for a phd in that school, you are really trying to appease the admissions department, you may not be allocated to a 'phd supervisor' yet.
But if you find which area you'd like to go into and the various 'leaders' in that field, you will probably notice they are not aligned to a 'top graduate school' and possibly deal with admission enquiries directly. (To quantify a leader check someones h-index score on google scholar then take with big pinch of salt)
What's different in this case is that they will most likely appreciate any additional work you've done which shows how interested you are in that particular field.
An admissions department on the other hand will probably look for GRE, GPA, awards, scholarships as ways to differentiate people.