"Ben Ha'arbayim" vs. "Ben Hashmashot"

Question

There seem to be two terms used to mean "twilight".

The Torah uses the term בן הערבים as in the time for the Mincha and Pesach offerings.

Talmudic literature uses the term בן השמשות

I know that there are differences in the length of twilight itself, halachically, as there are different opinions of tzet (when the stars appear.) However, I have generally understood that the time span of Ben Hashmashot is from when the sun begins to set (i.e. the "lowest" part of the sun is on the edge of the horizon) until tzet.

As בן הערבים is written in the Torah, it is obviously a much "older" term. I am assuming that there was no dispute as to exactly what that length of time was as there was an agreed / standard definition of when sunset begins and when tzet begins.

The Talmud brings in a debate of these two endpoints, which makes me assume that the definition of בן השמשות is not as clear.

My question is, do the Torah term and the Talmudic term refer to the same time span and these two terms are simply synonymous? Or are these referring to different time spans? If so, what are the differences?

Answer 1

Bein Ha'arbayim means the middle of the afternoon (Pesachim 58a, Sefaria):

אלא אמר רבא מצותו דתמיד משינטו צללי ערב מאי טעמא דאמר קרא בין הערבי' מעידנא דמתחיל שמשא למערב

Rather, Rabbi Yehoshua ben Levi’s source is rejected, and instead Rava said: The mitzva of the daily offering is from when the sun begins to descend westward so that the evening shadows slant eastward, shortly after midday. What is the reason for this? It is because the verse states: In the afternoon [bein ha’arbayim], which we understand to mean from the time that the sun begins to descend westward [ma’arav].

Bein Hasmashos means the end of the day, and possibly the beginning of night, "twilight" (Shabbos 34b, Sefaria):

ואיזהו בין השמשות משתשקע החמה כ"ז שפני מזרח מאדימין הכסיף התחתון ולא הכסיף העליון בין השמשות הכסיף העליון והשוה לתחתון זהו לילה דברי רבי יהודה ר' נחמיה אומר כדי שיהלך אדם משתשקע החמה חצי מיל רבי יוסי אומר בין השמשות כהרף עין זה נכנס וזה יוצא ואי אפשר לעמוד עליו

Nevertheless, the definition of twilight is uncertain. And what is twilight? From when the sun sets, as long as the eastern face of the sky is reddened by the light of the sun. If the lower segment of the sky has lost its color, and the upper segment has not yet lost its color, that is the twilight period. If the upper segment has lost its color, and its color equals that of the lower one, it is night; this is the statement of Rabbi Yehuda. Rabbi Neḥemya says: The duration of the twilight period is the time it takes for a person to walk half a mil after the sun sets. Rabbi Yosei says: Twilight does not last for a quantifiable period of time; rather, it is like the blink of an eye: This, night, enters and that, day, leaves, and it is impossible to calculate it due to its brevity.

For further details, I would suggest seeing the two Sugyas (which I quoted above) at length.