Are planes assigned different climb angles from the airport by the tower?
There can be many reasons. Flights taking off one after another:


have different destinations
have different weight and balance
have difference in wings and wingtips
have pilots with difference in skills
got different takeoff directions by ATC
are trying to avoid wake turbulence


Off all the reasons I mentioned above, perhaps wake turbulence might be playing more role about difference in takeoff angle. There are a ton of questions about wake turbulence, which is worth a read.