The difference between Impossibly and Inevitably

When used as adverbs, impossibly means not possibly, whereas inevitably means in a manner that is impossible to avoid or prevent.

check bellow for the other definitions of Impossibly and Inevitably

Impossibly as an adverb:

Not possibly; in an impossible manner.
Impossibly as an adverb:

To the point of impossibility.

Examples:

"The topology problem was impossibly difficult."
Impossibly as an adverb:

Contrary to what had been thought possible.

Examples:

"Impossibly, after the water receded, the cat was found asleep on a chair jammed in a tree."

Inevitably as an adverb:

In a manner that is impossible to avoid or prevent.

Examples:

"Inevitably, all creatures eventually die."

"The sun inevitably rises."

"Despite the town's best efforts, the dam inevitably gave way."

"The inevitably cold winter approaches."
Inevitably as an adverb:

As usual; predictably; as expected.

Examples:

"Inevitably, the next-door neighbour began to mow his lawn just as she lay down her head after a long night shift."

"The child inevitably began to cry when his mother went to work."

"The inevitably long line of customers queued for the latest 'Harry Potter'."