Final answer:
The punctuation style that omits the comma after the salutation and complimentary close in a letter is known as open punctuation.
Step-by-step explanation:
The punctuation style in a letter that omits the comma after the salutation and complimentary close is known as open punctuation. In contrast, closed punctuation includes the use of a comma after the salutation and a comma after the complimentary close. Semi-open punctuation and formal punctuation are not commonly used terms in this context. In the case of open punctuation, a letter would start with a salutation like 'Dear John' without a comma following the name and end with a complimentary close such as 'Sincerely' without a comma before the sender's name.