words - Did Aaron's staff turned into a snake or a crocodile?

In exodus 7 it says on verses 8-12:

ח וַיֹּאמֶר יְהוָה, אֶל-מֹשֶׁה וְאֶל-אַהֲרֹן לֵאמֹר. ט כִּי יְדַבֵּר אֲלֵכֶם פַּרְעֹה לֵאמֹר, תְּנוּ לָכֶם מוֹפֵת; וְאָמַרְתָּ אֶל-אַהֲרֹן, קַח אֶת-מַטְּךָ וְהַשְׁלֵךְ לִפְנֵי-פַרְעֹה--יְהִי לְתַנִּין. י וַיָּבֹא מֹשֶׁה וְאַהֲרֹן, אֶל-פַּרְעֹה, וַיַּעֲשׂוּ כֵן, כַּאֲשֶׁר צִוָּה יְהוָה; וַיַּשְׁלֵךְ אַהֲרֹן אֶת-מַטֵּהוּ, לִפְנֵי פַרְעֹה וְלִפְנֵי עֲבָדָיו--וַיְהִי לְתַנִּין. יא וַיִּקְרָא, גַּם-פַּרְעֹה, לַחֲכָמִים, וְלַמְכַשְּׁפִים; וַיַּעֲשׂוּ גַם-הֵם חַרְטֻמֵּי מִצְרַיִם, בְּלַהֲטֵיהֶם--כֵּן. יב וַיַּשְׁלִיכוּ אִישׁ מַטֵּהוּ, וַיִּהְיוּ לְתַנִּינִם; וַיִּבְלַע מַטֵּה-אַהֲרֹן, אֶת-מַטֹּתָם

Clearly talking about the staffs of both Aaron and the Egyptian sorcerers turning to crocodiles. Yet, later on verse 15 it says:

לֵךְ אֶל-פַּרְעֹה בַּבֹּקֶר, הִנֵּה יֹצֵא הַמַּיְמָה, וְנִצַּבְתָּ לִקְרָאתוֹ, עַל-שְׂפַת הַיְאֹר; וְהַמַּטֶּה אֲשֶׁר-נֶהְפַּךְ לְנָחָשׁ, תִּקַּח בְּיָדֶךָ.

Talking about the staff that turned into a snake. Never before any staff turned into a snake. And the only staff that turned into something before was Aaron's staff, that turned into a crocodile.

What exactly did Aaron's staff turned into? And what is the reason for the difference in the animal?

Answer

Shmos 4:3 When Hashem has Moshe throw his staff down, it turns into a Nachash. Here Aharon throws down his own staff and it turns into a Tanin. At the river, Moshe is told take the staff that originally was turned into a nachash on the mountain (his own staff) and warn Par'o.

Then in sentence 19, Hashem tells Moshe to tell Aharon to take his staff and stretch his hand out over the "waters of Egypt".

It seems that the point is that it does not matter which staff is being used as it is not a matter of a wizard using an object of power (which might be what the Egyptians thought) but Hashem causing the result.

Update:

I see that you also ask about the difference in usage between nachash and tanin.

The meforshim of the mountain miracles (such as Ramban) connect the snake and the tzora'as to the "loshon Hara" of Moshe saying "they won't believe me".

The tanin was considered the symbol of Egypt as shown in Yechezkel 29:3 (haftara of Va'Eira). Thus, what was being shown to Par'o and the court was the symbol of Egypt being under the control of Hashem.