Well, one difference is that do 'string' interprets 'string' as a file name, while eval 'string' interprets 'string' as Perl code:

$ perl -e 'do "print qq(foo\n)" or die qq($! $@)'
No such file or directory  at -e line 1.

$ perl -e 'eval "print qq(foo\n)" or die qq($! $@)'
foo
[download]

There are also other more subtle differences (such as do cannot see lexical variables in the enclosing scope, while eval can), but - believe it or not - it's all in the docs: do, eval :)