"Familiar with" is similar to "know". For example, "I am familiar with the daisy" is similar to "I know the daisy", where "know" has the meaning "am acquainted with". "Familiar to" is similar to "known by". For example, "I am familiar to Bob and Betty" is similar to "I am known by Bob and Betty". Here's an example to contrast the two. Consider the sentences "I am familiar with these woods" "I am familiar to these woods" The first says I know these woods well. The second says these woods know me well. It may seem strange to say the woods know me, but it makes sense. It is perhaps a bit poetic. It means I have been there so often that the trees know me.

The difference is in the way the sentence is constructed. ‘I am familiar with these things’ ie. I know about them, I have come across them before. ‘I’ ie. me is the subject, ‘these things’ is the object. ‘These things are familiar to me’ has the same meaning. ‘These things’ is the subject, ‘me’ is the indirect object.

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