Both Direct Method (DM) and Situational Language Teaching (SLT) are from "The Age of Methods" spanning from about 1950 to 1980.
Direct Method (Gouin and Berlitz), a 19th century approach, was revived at the beginning of the Age, after World War II. Situational Language Teaching hit its height in the middle (1960s) of the Age.
Direct Method Language Teaching
[DM has some ideological similarities with SLT.]
DM, originated as a reaction to Grammar-Translation method, presumes a second language is learned in the same way a first language is learned, though there are pragmatic difficulties with that presumption.
The premises are that (1) all instruction is given in the foreign language; (2) speaking and listening is emphasized; (3) vocabulary is simple, everyday words; (4) grammar is acquired inductively.
"Direct" refers to direct involvement with and interaction between language and life.
The role of the teacher is important as the intermediary who knows the foreign (target) language, who can expand vocabulary through exclusive use of the target language, and who can guide in the eventual inductive acquisition of the grammar behind the oral expressions.
Situational Language Teaching
SLT (also called Oral), British in origin, had a U.S. counter-part called Audio-Lingualism.
The premises are that (1) errors must be corrected; (2) learning must be oral, i.e., pronunciation and repetition; (3) written language comes after oral learning; (4) analysis of language, i.e., grammar, is not important for learning (it's important only after learning the oral language).
"Situational" refers to learning words in their "linguistic and cultural context" rather than in isolation from use and cultural setting.
The role of the teacher is important as error corrector, repetition drill leader, and context definer.
The Situational Language Learning approach (SLT), also known as the Oral approach, is a behaviorist (drill, practice, repetition) method of second or foreign language instruction in which structure and verbal repetition are the practices and skills that are mostly required from students in order to create the habit of speaking the words correctly. At least, that is the intention.
As opposed to its name, Situational Language has nothing to do with context, nor with being in an " immersion situation" like modern L2 teachers do these days. On the contrary, it contends that the management and memorization of over 2,000 sight words or frequent words place in a myriad of different speaking situations (for example, memorized dialogues, memorized poems, songs, and other sentences) will eventually help people conceptualize what they are saying. In not so many words, the SLT is the old-school type of L2 teaching where the teacher would bring a number of words in different scenarios to be used consistently in verbal communication. This was one of the methods of choice in early L2 teaching in the 1980's.
Direct instruction, or "the Direct Method", is the lecture-based method of teaching in which the teacher serves as the lecturer whereas the student has no option but to submit to listening and watching demonstrations of language usage via textbooks, videotapes, or audiotapes. Obviously the Direct Method is a counterproductive practice, as students are known to be more productive through inquiry-based instruction, through kinesthetic learning, and through consistent developmentally proper immersion. The Direct Method is sadly what is used in most colleges where the auditiorium serves as the classroom and when there are too many students to create a holistic lesson.
In all, neither the SLT nor the DI methods are good practices that would go in tandem with the model of 21st century instruction. They are both ancient methods that lacked the research value that we have today as L2 teachers and which has moved us to much better strategies that keep the student, and not the topic, at the center of instruction.
This is a great question. The main point is the method of instruction. The traditional teaching method for language learning is one that follows a systematic course. For example, you learn about nouns, then verbs, then adjectives and the like. After these building blocks, then you go in grammar and then into nuances of advanced grammar. All of this instruction is very neat and tidy.
A situation language method is a very different approach. The basic insight here is to learn language in a more natural way. The assumption here is that children learn language in situations. So, this approach is heavy on dialogues, role playing, skits, and other exercises that resemble life situations. Grammar is taught piecemeal, but it does not get the dominant focus. Often times, this approach also favors an immersion method, where only the target language is spoken class.