The main difference to consider would be that sympatric speciation occurs in the same habitat and population while allopatric speciation requires a geographical barrier between subsets of the population. In both, the populations have to be separated in a way that there is no gene flow between them. (this is an important point to make because those key words usually get you a mark in either case). In the case of allopatric speciation, the separation is a straightforward geographical one, like a river or valley. It's a little harder with sympatric speciation because this change can be behavioral, so for example a change in the mating display of a bird species, or involve different flowering times in plants. This all depends upon the context of the question but the important point is that it will occur in the same population. Here is where they converge- after this change, and lack of gene flow (two marks!) random mutations occur within members of the populations alleles. Different mutations will be advantageous in the different subsets of the population so different members of the species will survive to reproduce and pass on their alleles to their offspring. This follows the pattern of disruptive natural selection until the members of each group have become so genetically different they can no longer reproduce with each other and have fertile offspring, thus, speciation has occurred.