to do something vs doing something

[onetwothree]

Hi,
I've always been confused as to when to use "to do something" and when to use "doing something". Take this sentence for example.
What is the difference between these two?

1) She would be scared to death to see a spider.
2) She would be scared to death seeing a spider.

[jlinger]

1) She was afraid of the possibility of seeing a spider.
2) She actually saw the spider and was scared.