System Engineers may have a broader education (including Engineering, Mathematics and Computer science), while Software Engineers will come from a Computer Science or Computer Engineering background.
System engineer - one who works on the hardware parts of the computer..i.e, network connectionsassembling the systems,etc.. Software engineer - one who works / develops any code using his programming knowledge like c,java...GOT IT...
Software engineer engineers software parts of systems - he/she may require certain hardware capabilities or adapt to them but the actual building of HW is not really his/her field of interest. Systems engineer is accountable for overall system (HW,SW, documentation, users training) and realizes this accountability by orchestrating the efforts of various specialists (including SW engineers) by creating requirements, architecture, integration and testing.