They are two totally different forms. They both happen to use the word "to". Don't let that confuse you. They are completely different forms.
In the first sentence, "to be" is being used as a present infinitive. You can think of this as one word really, and in many languages (e.g. Spanish) the infinitive is one word.
In the second sentence the word "to" is a preposition. It is connecting "admit" with "being strict".
It is just a coincidence that the same word is used in these two different ways.