...הַחוֹבֵל בַּחֲבֵרוֹ וְהַמַּזִּיק מָמוֹנוֹ אַף עַל פִּי שֶׁשִּׁלֵּם לוֹ מַה שֶּׁהוּא חַיָּב לוֹ אֵינוֹ מִתְכַּפֵּר עַד שֶׁיִּתְוַדֶּה וְיָשׁוּב מִלַּעֲשׂוֹת כָּזֶה לְעוֹלָם...
...someone who injures a colleague or damages his property, does not attain atonement, even though he pays him what he owes until he confesses and makes a commitment never to do such a thing again...
Based on this halakhah, it appears that repaying damages is not enough to atone for any kind of monetary sin (whether physical [הַחוֹבֵל בַּחֲבֵרוֹ] or merely financial [הַמַּזִּיק מָמוֹנוֹ]) - one must also do vidui and commit to never repeat the sin (אֵינוֹ מִתְכַּפֵּר עַד שֶׁיִּתְוַדֶּה וְיָשׁוּב מִלַּעֲשׂוֹת כָּזֶה לְעוֹלָם).
In essence, in addition to paying what one owes, they must also do teshuvah. No other conditions for atonement are mentioned.
...עֲבֵרוֹת שֶׁבֵּין אָדָם לַחֲבֵרוֹ כְּגוֹן הַחוֹבֵל אֶת חֲבֵרוֹ אוֹ הַמְקַלֵּל חֲבֵרוֹ אוֹ גּוֹזְלוֹ וְכַיּוֹצֵא בָּהֶן אֵינוֹ נִמְחַל לוֹ לְעוֹלָם עַד שֶׁיִּתֵּן לַחֲבֵרוֹ מַה שֶּׁהוּא חַיָּב לוֹ וִירַצֵּהוּ.
אַף עַל פִּי שֶׁהֶחֱזִיר לוֹ מָמוֹן שֶׁהוּא חַיָּב לוֹ צָרִיךְ לְרַצּוֹתוֹ וְלִשְׁאל מִמֶּנּוּ שֶׁיִּמְחל לוֹ...
...Sins between man and man; for example, someone who injures a colleague, curses a colleague, steals from him, or the like will never be forgiven until he gives his colleague what he owes him and appeases him.
[It must be emphasized that] even if a person restores the money that he owes [the person he wronged], he must appease him and ask him to forgive him...
Based on this halakhah, it also appears that repaying damages is not enough to atone for any kind of monetary sin (whether physical [הַחוֹבֵל אֶת חֲבֵרוֹ], financial [גּוֹזְלוֹ], or even verbal [הַמְקַלֵּל חֲבֵרוֹ]) - one also must also appease their victim (אֵינוֹ נִמְחַל לוֹ לְעוֹלָם עַד שֶׁיִּתֵּן לַחֲבֵרוֹ מַה שֶּׁהוּא חַיָּב לוֹ וִירַצֵּהוּ).
No other conditions for atonement (i.e., teshuvah) are mentioned.
One can answer the implicit contradiction in these two halakhos as follows: There are three requirements to atone for monetary sins (whether physical, financial, or verbal):
1) One must pay what they owe (שִּׁלֵּם לוֹ מַה שֶּׁהוּא חַיָּב לוֹ/יִּתֵּן לַחֲבֵרוֹ מַה שֶּׁהוּא חַיָּב לוֹ)
2) One must do teshuvah (יִּתְוַדֶּה וְיָשׁוּב מִלַּעֲשׂוֹת כָּזֶה לְעוֹלָם)
3) One must appease their victim (ירַצֵּהוּ...צָרִיךְ לְרַצּוֹתוֹ וְלִשְׁאל מִמֶּנּוּ שֶׁיִּמְחל לוֹ)
אֵינוֹ דּוֹמֶה מַזִּיק חֲבֵרוֹ בְּגוּפוֹ לְמַזִּיק מָמוֹנוֹ. שֶׁהַמַּזִּיק מָמוֹן חֲבֵרוֹ כֵּיוָן שֶׁשִּׁלֵּם מַה שֶּׁהוּא חַיָּב לְשַׁלֵּם נִתְכַּפֵּר לוֹ. אֲבָל חָבַל בַּחֲבֵרוֹ אַף עַל פִּי שֶׁנָּתַן לוֹ חֲמִשָּׁה דְּבָרִים אֵין מִתְכַּפֵּר לוֹ. וַאֲפִלּוּ הִקְרִיב כָּל אֵילֵי נְבָיוֹת אֵינוֹ מִתְכַּפֵּר לוֹ וְלֹא נִמְחַל עֲוֹנוֹ עַד שֶׁיְּבַקֵּשׁ מִן הַנֶּחְבָּל וְיִמְחל לוֹ:
A person who damages a colleague's property cannot be compared to one who injures his physical person. When a person who damages a colleague's property pays him what he is obligated to pay him, he receives atonement. In contrast, when a person injures a colleague's physical person, paying him the five assessments is not alone sufficient to generate atonement. Even if the person who caused the injury sacrifices all the rams of Nevayot, he cannot generate atonement, nor is his sin forgiven until he asks the person who was injured to forgive him.
This halakhah bifurcates monetary sins into physical sins (מַזִּיק חֲבֵרוֹ בְּגוּפוֹ/חָבַל בַּחֲבֵרוֹ), which require appeasement, and merely financial sins (מַזִּיק מָמוֹנוֹ/הַמַּזִּיק מָמוֹן חֲבֵרוֹ), which do not.
At the very least, this explicitly contradicts the second source which specifies physical (הַחוֹבֵל אֶת חֲבֵרוֹ), financial (גּוֹזְלוֹ), and verbal (הַמְקַלֵּל חֲבֵרוֹ) monetary sins as requiring appeasement.
So which is it? Do all monetary sins require teshuvah and nothing else? Do all require appeasement and nothing else? Or do some require appeasement and while others don't?