The really big difference is that biology computes at overlapping time and distance scales, simultaneously. There are biological computational processes that occur at microseconds, to millennia, from fractions of a nanometer to kilometers all happing in concert and referencing each other. In the building of our own computational tools we generally try to avoid mixing physical scales like that. The analogies to computers aren't inherently wrong, they just need to mix in a lot more complexity.
Yes, we can break down aspects of biology into nice subsystems that we can define rules for - e.g. we have a pretty good idea of how DNA polymerase, or the ribosome carry out their duties (in isolation). It's when we start looking at the emergent properties of having all of these things in one larger system that our understanding starts to break down.
For laypeople, ill equiped to deal with high orders of complexity: spooky.
For people in the field: details.
For some audiences being accurate is less descriptive than being reductionist. Because if you lose your audience's attention, you've communicated no accuracy.