One translation of Maimonides states: "The Torah" refers to the Written Law; "the mitzvah," to its explanation. [God] commanded us to fulfill "the Torah" according to [the instructions of] "the mitzvah."5 "The mitzvah" is called the Oral Law.
In an article for Jewish Bible Quarterly, Jacob Chinitz provides this information:
This article will attempt to answer two questions: What is the meaning, or what are the meanings, of the word "Torah" when it occurs in the Torah? Is the Torah aware of itself as a book? There are 32 appearances of the word torah, or ha-torah, in the Pentateuch. In 11 of these, it is a common noun meaning "law" or "rule" in general, without specific reference to the Torah. In the other 21 appearances, the word refers to the Torah; once in Exodus and 20 times in Deuteronomy. In the first meaning, the word is used twice for law in general and nine times for a rule for a particular situation. In the second meaning, the word is used 10 times for the contents of the Torah, and 11 times for the material scroll of the Sefer Torah.
See "The Word 'Torah' in the Torah" by Chinitz.
Jewish Encyclopedia of 1906: The Torah receives its title from its contents, the name itself connoting "doctrine." The Hellenistic Jews, however, translated it by νόμος = "law" (e.g., LXX., prologue to Ecclus. [Sirach], Philo, Josephus, and the New Testament), whence came the term "law-book"; this gave rise to the erroneous impression that the Jewish religion is purely nomistic, so that it is still frequently designated as the religion of law. In reality, however, the Torah contains teachings as well as laws, even the latter being given in ethical form and contained in historical narratives of an ethical character.
Jewish Virtual Library.org: The Torah, or Jewish Written Law, consists of the five books of the Hebrew Bible - known more commonly to non-Jews as the "Old Testament" - that were given by G-d to Moses on Mount Sinai and include within them all of the biblical laws of Judaism. The Torah is also known as the Chumash, Pentateuch or Five Books of Moses.
The word "Torah" has multiple meanings including: A scroll made from kosher animal parchment, with the entire text of the Five Books of Moses written on it; the text of the Five Books of Moses, written in any format; and, the term "Torah" can mean the entire corpus of Jewish law. This includes the Written and the Oral Law.
From Oxford Bibliographies:
Law” or “Torah” (Hebrew) normally refers to instruction given by God to Moses at Sinai and preserved in the Pentateuch (Genesis through Deuteronomy), but can occasionally be used more broadly, even to refer to the Psalms, as in John 10:34. This article focuses on the former meaning and thus on works that deal with how New Testament writers (and also the historical Jesus) view the Law. Research on the latter has been greatly influenced by the way scholars have understood how Judaism at the time of Jesus and the early Christian movement viewed the Law. Stereotypical conflicts between Protestants and Catholics contributed to stereotypical views of Judaism and Law in much of the literature up to the mid-20th century, so that, at worst, Judaism was depicted as a religion where one earned status before God by meticulous observance of the Law, seen as burdensome, and had no real hope of forgiveness.
NABRE Footnote for Exodus 12:49: One law: the first appearance of the word torah, traditionally translated as “law,” though it can have the broader meaning of “teaching” or “instruction.” Elsewhere, too, it is said that the “alien” is to be accorded the same treatment as the Israelite (e.g., Lv 19:34).
Catholic Encyclopedia: Torah, [Image] (cf. Hiph. of [Image]), signifies first "direction, instruction", as, for instance, the instruction of parents (Proverbs 1:8), or of the wise (Proverbs 3:1). It is used chiefly in reference to the Divine instruction, especially through the revelation to Moses, the "Law", and to the teaching of the Prophets concerning the will of God. In the sense of law "Torah" refers only to the Divine laws. "Torah" is applied to the books containing the teaching of the Mosaic revelation and the Law, that is, the Pentateuch.
Brian Neil Peterson, Genesis as Torah, 21-22 of the electronic edition:
What is torah? Broadly defined torah means law or instruction (Gen 26:5; Exod 12:49; 13:9; 18:16 etc.). When assessing the Pentateuch, torah can be more narrowly defined as instruction in the ways and commands of YHWH (Exod 16:4; cf. 24:12).² Frank Crüsemann adds that “it comprises legal, moral, cultic, religious, theological and historical statements.”³ When most scholars speak of torah, it is quite clear that Genesis does not immediately come to mind.⁴ Instead they generally turn their focus to the obvious portions of the Pentateuch⁵ that engender the concept of law, namely, the Book of the Covenant (Exod 20:22—23:33); the Holiness Code of Leviticus 17–26; the Deuteronomic Law (Deut 12–26); or the Decalogue of Exodus 20 and Deuteronomy 5.⁶ A fine example of this is the approach used by Albrecht Alt (1883–1956), who when discussing the origins of the law in Israel only mentions Genesis in one passing footnote.
It is obvious that scholars struggle with using the term torah in its strictest sense when classifying the book of Genesis. Characteristic of this line of thought is Terence Fretheim’s definition of torah. He states, “The Hebrew word torah can be more properly used if it is broadly defined as instruction, and hence could include both law and narrative. But, given the usual meanings of the word ‘law,’ it should not be used as a shorthand reference to the Pentateuch in its entirety” (italics original).⁸ While I can appreciate what Fretheim is trying to say, I disagree with his conclusion that the word “law” should not encapsulate the whole of the Pentateuch. Not only are such definitions too narrow, they also fail to give proper weight to the torah instruction found in narratives throughout Genesis in particular. Moreover, these narrow definitions go against Jewish tradition, which identifies Genesis not only as part of the Torah, but as its very introduction! At the same time, care must be taken not to diminish the juridical force of the law in favor of its value as “religious instruction.”⁹ While using the term “instruction” in a general sense may help alleviate the tension, Genesis can also rightly be termed “law” or “case law” in a variety of situations where God in fact brought forth judgment (see next section below).¹⁰ Therefore, focusing mainly on the overt legal portions of the Torah as the primary legal instruction¹¹ within the Pentateuch is in fact to miss the importance of the implicit legal instruction present within the narratives of Genesis.¹² And, as just noted, such designations fail to take seriously the longstanding Jewish practice of labeling the entirety of the first five books of the Hebrew canon as Torah.