What's the difference between delayed branch and branch prediction?
Delayed branch and branch prediction are two different ways of mitigating the effects of a long execution pipeline. Without them, the pipeline needs to stall whenever a conditional branch is taken, because the instruction fetch mechanism can't know which instruction should be executed next after the branch instruction until the computations on which it depends are completed.

Delayed branch simply means that some number of instructions that appear after the branch in the instruction stream will be executed regardless of which way the branch ultimately goes. In many cases, a compiler can put instructions in those slots that don't actually depend on the branch itself, but if it can't, it must fill them with NOPs, which kills the performance anyway. This approach keeps the hardware simple, but puts a burden on the compiler technology.

Branch prediction is a more hardware-oriented approach, in which the instruction fetcher simply "guesses" which way the branch will go, executes instructions down that path, and if it later turns out to have guessed wrong, the results of those instructions are thrown away. Various systems have different ways of improving the accuracy of the guess. Sometimes the compiler puts a clue into the instruction stream, and sometimes the hardware keeps track of which way each branch has gone in the past.