Answer #1 (Ravina): No, both refer to Kodshim Kalim;

Beraisa #1 is like R. Yishmael (he learns meat from blood. Since blood cannot be offered when travelling, Kodshim meat becomes Pasul). Beraisa #2 is like Chachamim.

Answer #2: Both refer to Kodshei Kodoshim;

Beraisa #2 does not permit eating Kodshim in two encampments, rather, before taking down the Mishkan (this is not the simple meaning of the text, but Rashi and Tosfos say that we must understand it to mean this), and after taking down the Mishkan (this is like in two places);

One might have thought that (since the Mishkan is dissembled, there is no Kedushah to the Chatzer), and Kodshim are disqualified as if they left their proper place. The Beraisa teaches, this is not so.

Suggestion: Perhaps they are disqualified!

Rejection "V'Nasa Ohel Mo'ed" - even though it is in transit, it has the Kedushah of Ohel Mo'ed.

(Rav Huna): The Mizbe'ach in Shilo was of stones.

(Beraisa - R. Eliezer ben Yakov): Three verses say "Avanim", to teach about three Mizbechos that were (Rashi - permitted to be) made of stones, in Shilo, in Nov and Giv'on (we learn both of these from one verse, since both were Bamos and not proper Mizbechos) and in the Beis ha'Mikdash.

Question (Rav Acha bar Ami - Beraisa): The fire that descended from Shamayim (to the Mizbe'ach ha'Nechoshes) in the days of Moshe did not cease, until a new fire descended when Shlomo built (a new Mizbe'ach in) the Beis ha'Mikdash;

Shlomo's fire did not cease until the days of Menasheh. (Even though his grandfather Achaz abolished the Avodah (Sanhedrin 103b), we must say that the fire did not cease until Menasheh's reign.)

According to Rav Huna, Moshe's fire ceased when they built a new Mizbe'ach in Shilo!

Answer #1: Rav Huna's teaching is according to R. Noson.

(Beraisa - R. Noson): The Mizbe'ach in Shilo was made of copper. It was hollow, and they filled it with stones.

Answer #2 (Rav Nachman bar Yitzchak): The Beraisa says that Moshe's fire did not cease. It was not idle. (Even though (in Shilo) Korbanos were not brought on the Mizbe'ach ha'Nechoshes, rather, on a stone Mizbe'ach.)

Question: What is the meaning of 'it was not idle'?

Answer #1 (Rabanan): It spewed forth flames to the stone Mizbe'ach to consume the Korbanos.

Answer #2 (Rav Papa): Sometimes the fire would be on one Mizbe'ach, and sometimes on the other.

(Mishnah): When the exiles returned (with Ezra, to build the second Beis ha'Mikdash) they added four Amos onto the Mizbe'ach on the south side, and four Amos on the west side. The addition was an 'L' shape.

Question: Why did they make it bigger?

Answer #1 (Rav Yosef): (The dimensions of) Shlomo's Mizbe'ach were not big enough.

Objection (Abaye): In the first Mikdash, "Yehudah v'Yisrael Rabim ka'Chol Asher Al ha'Yam", yet the Mizbe'ach was big enough. In the second Mikdash "Kol ha'Kahal k'Echad Arba Ribo..." (there were less than 50,000 people), all the more so it was big enough!

Answer (Rav Yosef): In the first Mikdash, fire of Shamayim consumed the Korbanos (supernaturally) quickly. This did not happen in the second Mikdash.

Answer #2 (Ravin): (In the first Mikdash, Nesachim would flow into Shisim (a pit south-west of the Mizbe'ach.) They enlarged the Mizbe'ach in order that the Shisim would be within (under) the Mizbe'ach;

At first, they expounded "Mizbe'ach Adamah" - there cannot be any gap beneath it;

Later, they reasoned that drinking ('consumption' of libations) should be like eating (Korbanos that are burned, i.e. within the boundaries of the Mizbe'ach).

"Mizbe'ach Adamah" teaches that the Mizbe'ach cannot be built over domes or tunnels (that are not needed for the Mizbe'ach).