Other nicknames that [people use] to show praise to G-D with them, for example, Gracious and Merciful (Shemos 34:6)
|ו וַיַּעֲבֹר יְהוָה עַל-פָּנָיו, וַיִּקְרָא, יְהוָה יְהוָה, אֵל רַחוּם וְחַנּוּן--אֶרֶךְ אַפַּיִם, וְרַב-חֶסֶד וֶאֱמֶת.||6 And the LORD passed by before him, and proclaimed: 'The LORD, the LORD, God, merciful and gracious, long-suffering, and abundant in goodness and truth;|
|יז כִּי, יְהוָה אֱלֹהֵיכֶם--הוּא אֱלֹהֵי הָאֱלֹהִים, וַאֲדֹנֵי הָאֲדֹנִים: הָאֵל הַגָּדֹל הַגִּבֹּר, וְהַנּוֹרָא, אֲשֶׁר לֹא-יִשָּׂא פָנִים, וְלֹא יִקַּח שֹׁחַד.||17 For the LORD your God, He is God of gods, and Lord of lords, the great God, the mighty, and the awful, who regardeth not persons, nor taketh reward.|
The Faithful (Devarim 7:9)
|ט וְיָדַעְתָּ, כִּי-יְהוָה אֱלֹהֶיךָ הוּא הָאֱלֹהִים: הָאֵל, הַנֶּאֱמָן--שֹׁמֵר הַבְּרִית וְהַחֶסֶד לְאֹהֲבָיו וּלְשֹׁמְרֵי מִצְוֹתָו, לְאֶלֶף דּוֹר.||9 Know therefore that the LORD thy God, He is God; the faithful God, who keepeth covenant and mercy with them that love Him and keep His commandments to a thousand generations;|
Jealous (Shemos 20:4)
|ד לֹא-תִשְׁתַּחֲוֶה לָהֶם, וְלֹא תָעָבְדֵם: כִּי אָנֹכִי יְהוָה אֱלֹהֶיךָ, אֵל קַנָּא--פֹּקֵד עֲוֹן אָבֹת עַל-בָּנִים עַל-שִׁלֵּשִׁים וְעַל-רִבֵּעִים, לְשֹׂנְאָי.||4 thou shalt not bow down unto them, nor serve them; for I the LORD thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate Me;|
Strong (Yirmiyahu 50:34)
|לד גֹּאֲלָם חָזָק, יְהוָה צְבָאוֹת שְׁמוֹ--רִיב יָרִיב, אֶת-רִיבָם: לְמַעַן הִרְגִּיעַ אֶת-הָאָרֶץ, וְהִרְגִּיז לְיֹשְׁבֵי בָבֶל.||34 Their Redeemer is strong, the LORD of hosts is His name; He will thoroughly plead their cause, that He may give rest to the earth, and disquiet the inhabitants of Babylon.|
and similar names are like other words in the holy [language] and they are permitted to be erased.
The question to ask here is why are these names of G-D allowed to be erased, but the names stated in the second halacha are not allowed to be erased? In short, the names in the second halacha refer to G-D himself. They are descriptions (except yud hey vav hey) of G-D, but they are not admirations or praises.
However, the names referred to in this halacha are purely names associated with praise. No one who speaks with G-D uses these names solely to refer to G-D, but they use these names to praise and show admiration towards G-D. As we see in the Gemara in Berachos (33b):
A certain [reader] went down in the presence of R. Hanina and said, O God, the great, mighty,
terrible, majestic, powerful, awful, strong, fearless, sure and honoured. He waited till he had
finished, and when he had finished he said to him, Have you concluded all the praise of your
Master? Why do we want all this? Even with these three that we do say, had not Moses our Master
mentioned them in the Law and had not the Men of the Great Synagogue come and inserted them
in the Tefillah, we should not have been able to mention them, and you say all these and still go on!
It is as if an earthly king had a million denarii of gold, and someone praised him as possessing silver
ones. Would it not be an insult to him? (Translation from Soncino Gemara)
It seems to me that the names in the second halacha are names we use to refer to G-D either because that is His name (Yud hey vav hey) or they are descriptors of G-D. However, the names in this halacha are how we relate to G-D. We see G-D as Awesome, Merciful, Faithful, Great, Powerful, etc because this is how we perceive Him.
If we were not here G-D would still be Shaddai, Tzivaos, EL, Yud Hey Vav Hey, Elokim, Alef Dalet Nun Yud, Eloka. However, if human's were not around He could not be described as Merciful, Gracious, Mighty, Awesome, Faithful, etc because these are human praises. Therefore, these names are not as inherently descriptive of G-D.