The short answer is that reason, logic, and dialectic are conceptually overlapping.
Reason is often taken to be the process a philosopher engages is and is a property of intelligence. Therefore one reasons according to logic to perform the dialectic.
Logic is taken by many to be the formal properties of reason, in the least formal sense informal logic and in the most formal sense formal logic.
Dialectic is taken to be a methodlogy of philosophy which the reasonable person uses to demonstrate good logic, taken either as valid and sound in the deductive case or strong and cogent in the inductive case. The best forms of inference are taken to be parsimonious, salient, strong, and valid since they range across a whole collection of smaller arguments. From WP:
Dialectic (Greek: διαλεκτική, dialektikḗ; German: Dialektik), also known as the dialectical method, refers originally to dialogue between people holding different points of view about a subject but wishing to arrive at the truth through reasoned argumentation. Dialectic resembles debate, but the concept excludes subjective elements such as emotional appeal and rhetoric.1 It has its origins in ancient philosophy and continued to be developed in the Middle Ages... In the modern period, Hegelianism refigured "dialectic" to no longer refer to a literal dialogue. Instead, the term takes on the specialized meaning of development by way of overcoming internal contradictions. (emphasis mine)
So, in the original sense, dialectic was just the informal use of reason to have a conversation in a very broad way looking to focus on the logos of an argument. By the time of Kant, Husserl, Frege, and Hegel, the notion of linguistic and logical analysis began to enter the fore where it was recognized that philosophy used language to root out contradiction.
Today, the analytic tradition takes the location of logical contradiction in language as a sancrosanct principle. There are whole bodies of work around Russell's paradox, category mistakes, and fallacy that those who follow the linguistic turn appeal to in their argumentation. In natural language ontology (SEP), for instance, one finds such topics as quantifier variance which relies on and looks to logical contradiction for explaining differences in ontological commitment in natural languages.
Hegel was attempting, like Frege with symbols, to put the notion of logical contradiction on a more scientific basis than the Ancient Greeks.