What do "as both" and "both as" mean?

Sometimes it's used as "as both" and sometimes as "both as", examples:

His performance both as a captain and as a player was terrible.

or

I start with my own story, as both a means of explaining where I come from and, I hope, a way to show why I believe everyone is capable of change.

Do they have different meanings in the examples and with what words could they be replaced keeping the same sense of those sentences?

The most certain rule is to use parallel forms after the words "both" and "and" in such a construction. By that rule, either say,

• both as captain and as (a) player

or

• as both captain and (a) player.

Certainly there are times when the "rule" is broken. If it is clear that a particular word ("as" in this case) has been left to be "understood", most people will find it natural, but some still may think it is an error. In a context (probably formal) where you really are worried about that possibility, it would be best to go for strict parallelism with the "both a" and "as" constructs.