What Are The Main Differences Between Multiprocessor And Multitasking?

The main difference is in the number of processors. Multitasking is a way to make progress on a number of tasks "at once" on a single processor. On a properly programmed multiprocessor, the tasks are actually run in parallel on multiple processors, not just divided into little interleaved chunks.

Suppose we have 3 tasks, A, B, and C. If each of these can be divided into sequential pieces, for example, A0, A1, A2, A3 ..., then the execution sequence on a multitasking machine might be
  processor 1: A0, B0, C0, B1, C1, A1, B2, C2, B3, C3, A2, ... (task A is given lower priority)

On a parallel (multiprocessor) machine, the tasks might be allocated to processors on a 1:1 basis
  processor 1: A
  processor 2: B
  processor 3: C
Where each task runs to completion on its assigned processor, without interruption.

Multitasking is of some advantage when the mix of tasks is such that the tasks running at any given time do not compete for the same machine resources. If one has to wait on input or output, the other can run until it is blocked by some resource request. This can keep the machine busy while it would otherwise be waiting idly.