Ad orationem, Lat. oratio, “speech, discourse”
Ad litteram, Lat. littera, “letter; writing”
Both labels can refer to written or oral speech
1. In law
2. In everyday argument
In everyday conversation, the label to the letter (ad litteram) refers to a second speech turn based upon what has been expressly (“verbally”) said, word for word, by the other party, leaving aside what was meant by the first speaker. This is the case of indirect speech acts of request, softened as a question
L1: – Can you pass me the salt?
L2: – Yes
But L2 does not pass the salt shaker to L1. L2 answered the letter , without taking into account the fact that L1 was not asking him about his ability to pass the salt shaker, but was asking him to pass the salt (to do something).
In an argumentative situation, the label ad litteram response is used to refer to a response, that sticks strictly sticks « to the letter » of what was said by the opponent, without trying to « understand » what the latter wanted to say:
The police : — Just tell me so-and-so did it, and I release you
The suspect : — « So-and-so did it »
The suspect said to the letter what the police asked him to say in order to be released. He answered the letter, but he probably won’t be released. In more serious circumstances:
I don’t know what you meant, I just anwered what you said.
The suspect fulfils his turn of speech, and returns the floor to the accuser, who must rephrase what he wants to say.
The reply addresses the word and sentence meaning and not the speaker’s meaning, that is the spirit or intention of what the other party actually said.
Appealing to the letter — Based on a methodical and exclusive exercise of reason (ad judicium@), the argument on the merits (ad rem@, to the matter@) deals substantially with the the case. The argument to the letter evades the issue by dealing only with its formal aspects.
This strategy can be used as a disorientating move, serving a destructive strategy. It bypasses the significant content of the intervention by focusing on the letter of the speech. It can even turn the letter of the speech against the intention of the speaker.
This maneuver is opposed to a response that charitably considers the intention of the discourse and does not seek to take advantage of a bad formulation.
— SITUATION: A dispute about the legal and ethical management of science funding
1) Research in domain B is conditioned by a statutory provision S prohibiting research likely to lead to Type U results.
2) A research group submits to institution I a research project in domain B. The research objectives are defined in the research proposal accompanying the funding application. The funding is granted.
2) This research produces a result X
— CLAIM: X result is a U-type result. R did Type U research, and I funded type U research. Both knowingly broke the statutory provision.
Does the research U contravene the statutory provision prohibiting research leading to Type U results?
— ANSWER NO: Strict meaning, appeal to the letter of the relevant text.
NO. U emerged; it was something unexpected. As you can read, there is nothing about a Type U research in the terms of reference given to the researchers. No research likely to produce Type U results is included in the terms of reference.
That kind of unexpected things regularly happens in scientific research.
— ANSWER YES: Intentional interpretation, S. Motives and good reasons
THEY DO. U did not “emerge”, it was intentionally produced.
(1) Our panel of top-level scientist says that a competent researcher can foresee that Type U results would follow from the objectives as defined in the specifications.
(2) The reference terms does not explicitly refer to U as an objective of the research in order to avoid the obvious legal and political consequences.
(3) But they describe work that matches the commonly accepted definition of U and meet the criteria for Type U research according to distinguished members of the relevant scientific community.
Conclusion: They had an hidden agenda. They actually did Type U research, whether they used that phrase or not. 
 This example is derived from Glenn Kessler, “The repeated claim that Fauci lied to Congress about ‘gain-of-function’ research”. The Washington Post, Oct. 29, 2021.