How 'd U differentiate these phrases; 'compiling report', 'writing report'?

compilation of report means you prepared a summary (you can say Conclusion). 

while report writing is a phenomena in which you put detailed work for the ease of reader.

When I am asked for compiling a report, I summarise, provide graphical representation of the data after normalising and analysis to reach a conclusion based on the data.

When i write a report, this could mean a brief understanding of the subject or making a data sheet.