Yep -
1. Midrash aggadah - narrative midrash: "interpreting biblical narrative, exploring questions of ethics or theology, or creating homilies & parables based on the texts"; and
2. Midrash halacha - attempting "to clarify or extend a law beyond the conditions assumed in the Hebrew Bible, and to make connections between then current practice and the biblical text. It made possible the creation and acceptance of new liturgies and rituals which de facto replaced sacrificial worship after the fall of the Second Temple" (and, for Judaism, "the maintenance of continuity by linking those practices to the words of the Torah", but that would not have happened in the development of or application to Christianity).
These are general categorisations: each tends to contain components of the other.
Interestingly, "Midrash halacha from the two centuries following the fall of the Temple was collected in three books — the Mekhilta on Exodus, the Sifra [book] on Leviticus, and the Sifrei [books] on Numbers and Deuteronomy — known as the tannaitic midrashim. (The tannaim [tanna, sing.] were the rabbis from the time of the Mishnah, edited in approximately 200 CE.)" - https://www.myjewishlearning.com/article/midrash-101/
and, 'Midrash Aggadah', "The type of midrash most commonly referred to (as in, “There is a midrash which says…”) is from the collections of midrash aggadah, most of which were compiled between about 200 and 1000 C.E. (Many midrashim circulated orally before then). Midrash aggadah may begin its exploration with any word or verse in the Bible. There are many different methods of interpretation and exposition."
- and, ".. midrash aggadah also appears throughout the two Talmuds. Midrash Rabbah, the “Great Midrash,” is the name of the collections linked to the five books of the Torah and the “Five Scrolls” (Esther, Song of Songs, Ruth, Lamentations, and Ecclesiastes) read on holidays. Some of these works read like verse-by-verse commentaries. Others may have originated in sermons linked to the weekly Torah reading."
https://www.myjewishlearning.com/article/midrash-101/
Much Aggadah, often mixed with foreign elements, is found in the Apocrypha, the Pseudepigrapha, the works of Josephus and Philo, and the remaining Judæo-Hellenistic literature; but aggadic exegesis reached its highest development in the great epoch of the Mishnaic-Talmudic period, between 100 and 550 CE.
https://en.wikipedia.org/wiki/Aggadah#Development
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Akiva ben Yosef (Hebrew: עקיבא בן יוסף, c. 50–135 CE) widely known as
Rabbi Akiva (רבי עקיבא), was a tanna of the latter part of the first century and the beginning of the second century (the third tannaitic generation). Rabbi Akiva was a leading contributor to the Mishnah and to Midrash halakha. He is referred to in the Talmud as Rosh la-Hakhamim, "Chief of the Sages". He was executed by the Romans in the aftermath of the Bar Kokhba revolt ...
The greatest tannaim of the middle of the second century came from Akiva's school, notably Rabbi Meir, Judah bar Ilai, Simeon bar Yochai, Jose ben Halafta, Eleazar ben Shammai, and Rabbi Nehemiah. Besides these, Akiva had many disciples whose names have not been handed down, but the Aggadah variously gives their number as 12,000, 24,000, and 48,000.
Biblical Canon
Akiva was instrumental in drawing up the canon of the Tanakh. He protested strongly against the canonicity of certain of the Apocrypha, the Wisdom of Sirach, for instance, in which passages קורא is to be explained according to Ḳid. 49a, and חיצונים according to its Aramaic equivalent ברייתא; so that Akiva's utterance reads, "He who reads aloud in the synagogue from books not belonging to the canon as if they were canonical," etc. But he was not opposed to a private reading of the Apocrypha, as is evident from the fact that he himself makes frequent use of Sirach. Akiva stoutly defended, however, the canonicity of the Song of Songs, and Esther ...
Aquila, meanwhile, was a disciple of Akiva and, under Akiva's guidance, gave the Greek-speaking Jews a rabbinical Bible. Akiva probably also provided for a revised text of the Targums; certainly, for the essential base of the Targum Onkelos, which in matters of Halakah reflects Akiva's opinions completely.
Akiva as systematizer
Akiva worked in the domain of the Halakha, both in the systematization of its traditional material and in its further development. The condition of the Halakah, that is, of religious praxis, and indeed of Judaism in general, was a very precarious one at the turn of the 1st century of the common era ... The Jewish Encyclopedia states that according to a tradition which has historical confirmation, it was Akiva who systematized and brought into methodic arrangement the Mishnah, or Halakah codex; the Midrash, or the exegesis of the Halakah; and the Halakot, the logical amplification of the Halakah.
https://en.wikipedia.org/wiki/Rabbi_Akiva
.
Akiva ben Yosef (Hebrew: עקיבא בן יוסף, c. 50–135 CE) widely known as
Rabbi Akiva (רבי עקיבא), was a tanna of the latter part of the first century and the beginning of the second century (the third tannaitic generation). Rabbi Akiva was a leading contributor to the Mishnah and to Midrash halakha. He is referred to in the Talmud as Rosh la-Hakhamim, "Chief of the Sages". He was executed by the Romans in the aftermath of the Bar Kokhba revolt ...The greatest tannaim of the middle of the second century came from Akiva's school, notably Rabbi Meir, Judah bar Ilai, Simeon bar Yochai, Jose ben Halafta, Eleazar ben Shammai, and Rabbi Nehemiah. Besides these, Akiva had many disciples whose names have not been handed down, but the Aggadah variously gives their number as 12,000, 24,000, and 48,000.
Biblical Canon
Akiva was instrumental in drawing up the canon of the Tanakh. He protested strongly against the canonicity of certain of the Apocrypha, the Wisdom of Sirach, for instance, in which passages קורא is to be explained according to Ḳid. 49a, and חיצונים according to its Aramaic equivalent ברייתא; so that Akiva's utterance reads, "He who reads aloud in the synagogue from books not belonging to the canon as if they were canonical," etc. But he was not opposed to a private reading of the Apocrypha, as is evident from the fact that he himself makes frequent use of Sirach. Akiva stoutly defended, however, the canonicity of the Song of Songs, and Esther ...
Aquila, meanwhile, was a disciple of Akiva and, under Akiva's guidance, gave the Greek-speaking Jews a rabbinical Bible. Akiva probably also provided for a revised text of the Targums; certainly, for the essential base of the Targum Onkelos, which in matters of Halakah reflects Akiva's opinions completely.
Akiva as systematizer
Akiva worked in the domain of the Halakha, both in the systematization of its traditional material and in its further development. The condition of the Halakah, that is, of religious praxis, and indeed of Judaism in general, was a very precarious one at the turn of the 1st century of the common era ... The Jewish Encyclopedia states that according to a tradition which has historical confirmation, it was Akiva who systematized and brought into methodic arrangement the Mishnah, or Halakah codex; the Midrash, or the exegesis of the Halakah; and the Halakot, the logical amplification of the Halakah.
https://en.wikipedia.org/wiki/Rabbi_Akiva
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