They are simply different forms of the same verb:
Be is the dictionary form and the bare infinitive (infinitive without 'to') form of the verb.
To be is the infinitive form.
Do is the dictionary form, the bare infinitive form, and the simple present form (except for 3rd person does) of the verb.
To do is the infinitive form.
What else would you like to know about these forms?
Student or Learner