First off, to be obvious, discrete-time conv is for discrete-time signals and cont-time conv... - i'm sure you knew this. The real difference is that for cont-time, integration is required, since it's continuous - you're just summing area. For discr-time, it's just a summation. Discrete-time conv is a lot easier since you're just multiplying points/delta func's and adding them up - shift again and repeat the process. I hope that answered your question.
