halacha - Why is fish and milk permitted but not poultry and milk?

E.g. Chicken and milk is forbidden, but fish and milk is permitted. (Some Hassidim and Sefardim do not mix fish and milk as I understand it).

If going off the common answer of not to confuse chicken with meat, why is fish any different?

Answer

About quails they eat in the desert what says the verse? Bamidbar (11, 33).

הַבָּשָׂר עוֹדֶנּוּ בֵּין שִׁנֵּיהֶם טֶרֶם יִכָּרֵת וְאַף יְהֹוָה חָרָה בָעָם וַיַּךְ יְהֹוָה בָּעָם מַכָּה רַבָּה מְאֹד:

Let's learn a little passage of Gemoro.
you start with a Mishno Chulin (8, 1)

ח,א כל הבשר אסור לבשל בחלב, חוץ מבשר דגים וחגבים; ואסור להעלותו עם הגבינה על השולחן, חוץ מדגים וחגבים. הנודר מן הבשר, מותר בבשר דגים וחגבים

The mishna added that in common language, fish is not called meat (in the contextual language of the Tana).
A little further the Mishnah tells us:

המעלה את העוף ואת הגבינה על השולחן, אינו עובר בלא תעשה.

to take poultry with cheese on the table is not prohibited from the Torah

further the Mishnah teaches us

רבי עקיבה אומר, חיה ועוף אינן מן התורה, שנאמר "לא תבשל גדי, בחלב אימו" "לא תבשל גדי, בחלב אימו" (שמות כג,יט; שמות לד,כו; דברים יד,כא): שלושה פעמים--פרט לחיה, ולעוף, ולבהמה טמאה. רבי יוסי הגלילי אומר, נאמר "לא תאכלו כל נבילה" (דברים יד,כא), ונאמר "לא תבשל גדי, בחלב אימו" (שם)--את שהוא אסור משום נבילה, אסור לבשל בחלב; עוף, שהוא אסור משום נבילה, אינו דין שיהא אסור לבשל בחלב: תלמוד לומר "בחלב אימו"--יצא העוף, שאין לו חלב אם

After Rabbi Yossi Haglili, we would think that poultry is the equivalent of lamb with regard to the legislation of Bassar Behalav. This is because poultry can have the status of carcass (a special kind of impurity and more things. This is not the case for fish). But the verse refers to the milk of the mother and mothers of birds don't product milk.
The Gemoro Daf 116A says that Rabbi Yehudo ben Betera permits poultry with milk, and may be Rabbi Yossi Haglili also.

So Fish may not be carcass (Neveylo) and is not linked with the verse that prohibit Bossor Becholov. (We may read an important translation of the mishna in tosfoth that undertand that Rabi Akiva comes to counter an opinion that poultry is prohibed min Hatorah as lamb.in Mechilta at the end of Mishpotim, this is the opinion of Rabbi Yoshia. It is not the place for an extended explanation.)

Fish with milk in the Minhogim:
Chulin 111B

איתמר דגים שעלו בקערה רב אמר אסור לאכלן בכותח ושמואל אמר מותר לאכלן בכותח Blockquote

Fishes that has absorbed (we will not discuss here the nature of the absorption) meat, if this absorbtion is significant, we do not eat them with a kind milky condiment.
This says that fish alon can be eaten with milk! The Beyth Yossef YD 88,3 says that following the Rashbo in torath Habayt it is prohibited due to a danger (a medical threat as for fish with meat, a danger to become leprous.). For danger there arre Poskim that prohibit indirect absorption to. (for a further topic)

In SA OC 173, the Magen Avrohom SK 1, emits doubts about the sustainability of such medical considerations in actual world. (His subject is fish with meat but the Beyth Yossef in YD 88 compar the two, that is fish and meat and fish and milk) That is, the actual medicine don't identify any threat in this. But don't counter the din.