She is the baker to have made this unique bread.
She is the baker who made this unique bread.
What is the difference? Can I use 'to' and 'relative pronouns' interchangeably?
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Your first sentence is not something you will come across much, though it is close. I think there are two problems here.
The first is that sentences of the form of your first, even when they are standard/natural, don't mean the same thing as the second sort:
I'm the man to fix this problem.
I'm the man who will fix this problem.
I'm the man (who is) fixing this problem.
The first is used to say that someone is the right person for the job. It is, in essence, expressing purpose. It is not used where you are expressing certainty about who will do something or is doing something. This brings us to the second problem. You can use this sort of expression in the past, but it wouldn't be used where you knew what had happened, but were speculating about it, or passing comment on a known fact. If you just want to state a known fact, you use something of the form of your second sentence. Your first sentence would appear to be saying "she is a baker whom one might expect to have made this unique bread", but in practice it just doesn't get used that way very much (more in speech then in writing, I think). You can get to a more normal way of saying it if you phrase it differently, or use extra words, for example:
She's just the sort of baker to have made this unique bread.
This might be used to express a theory about something uncertain, or to indicate that the information you've been given makes sense:
Helen made this? Well, she's just the sort of baker to have made this unique bread.
Your second example is expressing certainty, not positing a theory or commenting on one.
There is no general interchangeability of relative pronouns and to. They are used for different things.
 She is the baker to have made this unique bread.
 She is the baker who made this unique bread.
 is a straightforward relative construction, where the relative clause modifies "baker".
But  is ungrammatical since the infinitival clause cannot function as a relative clause unless a modifier such as "only", "next", "last" or an ordinal number is inserted:
 She is the first baker to have made this unique bread,
which is the equivalent of
She is the first baker who made this unique bread.