344 reproduces R. Ishmael's view on the question at issue. As for the halakhic midrash, it may be said that, in contradistinction to the aggadic part, the collector used, aside from R. Ishmael's midrash, that of R. Simeon.
344 expresses R. Ishmael's stance on the central issue. Conversely, the halakhic midrash diverges from the aggadic component in that it draws upon R. Simeon's commentary, distinct from R. Ishmael's insights.