Reasoning Vs Inference

Inference:
Inference is a general term representing the derivation of new knowledge from existing knowledge and axioms (i.e., rules of derivation) within a single step, and can be one of many kinds, such as, induction, deduction and abduction. For example, "modus tollens" is a rule of inference. Thus, one inference is the derivation of new knowledge using a single step using modus tollens.
Inference is about taking in data and trying to draw a conclusion based on the limited information you have in a situation where not all the data is given.

Reasoning:

Reasoning is in context of a goal (e.g., decide whether a propositional formula is satisfiable or not)  and is carried out via a search process involving multiple inferences. Choices during such search have to be made such as which axiom to "fire" along with which knowledge in order to derive new knowledge.

Resolution is a particular kind of reasoning involving the "resolution rule".

Reasoning is about drawing conclusions using your own mind.

Types of Reasoning

Deduction: In this form of reasoning a person starts with a known claim or general belief, and from there determines what follows. Essentially, deduction starts with a hypothesis and examines the possibilities within that hypothesis to reach a conclusion. Deductive reasoning has the advantage that, if your original premises are true in all situations and your reasoning is correct, your conclusion is guaranteed to be true. However, deductive reasoning has limited applicability in the real world because there are very few premises which are guaranteed to be true all of the time.

A syllogism is a form of deductive reasoning in which two statements reach a logical conclusion. An example of a syllogism is, “All dogs are mammals; Kirra is a dog; therefore, Kirra is a mammal.”

Induction:Inductive reasoning makes broad inferences from specific cases or observations. In this process of reasoning, general assertions are made based on specific pieces of evidence. Scientists use inductive reasoning to create theories and hypotheses. An example of inductive reasoning is, “The sun has risen every morning so far; therefore, the sun rises every morning.” Inductive reasoning is more practical to the real world because it does not rely on a known claim; however, for this same reason, inductive reasoning can lead to faulty conclusions. A faulty example of inductive reasoning is, “I saw two brown cats; therefore, the cats in this neighborhood are brown.”

Abduction: Abductive reasoning is based on creating and testing hypotheses using the best information available. Abductive reasoning is used in a person’s daily decision making because it works with whatever information is present—even if it is incomplete information. Essentially, this type of reasoning involves making educated guesses about the unknowable from observed phenomena. Examples of abductive reasoning include a doctor making a diagnosis based on test results and a jury using evidence to pass judgment on a case: in both scenarios, there is not a 100% guarantee of correctness—just the best guess based on the available evidence.

The difference between abductive reasoning and inductive reasoning is a subtle one; both use evidence to form guesses that are likely, but not guaranteed, to be true. However, abductive reasoning looks for cause-and-effect relationships, while induction seeks to determine general rules.