The word פת means "piece". (As I don't believe in coincidence, I think the English word "piece" may have come from the Hebrew, in some way!)
See Radak on Genesis 18:5:1 (Sefaria English translation) - Hebrew & English excerpted by me:
ואקחה פת לחם, כי הנה אברהם אמר פת לחם שפירושו חתיכת לחם ולא אמר
לחם כמו שאמר מעט מים כמו שפירשנו. ואקחה פת לחם
Avraham spoke about a piece of bread, whereas in fact he served
a sumptuous meal. He had even understated the amount of bread he
would serve by not saying ואקח לחם, but ואקחה פת לחם, a reference to
less than a whole loaf.
Further support for the concept that the word means "piece" is Leviticus 2:6 (Sefaria English):
פָּת֤וֹת אֹתָהּ֙ פִּתִּ֔ים וְיָצַקְתָּ֥ עָלֶ֖יהָ שָׁ֑מֶן מִנְחָ֖ה
Thou shalt break it in pieces, and pour oil thereon; it is a
As your question appears to be general, it seems that Tanach's use of the term refers to the term "piece". See Ruth 2:14:
וַיֹּאמֶר֩ לָ֨ה בֹ֜עַז לְעֵ֣ת הָאֹ֗כֶל גֹּ֤שִֽׁי הֲלֹם֙ וְאָכַ֣לְתְּ
מִן־הַלֶּ֔חֶם וְטָבַ֥לְתְּ פִּתֵּ֖ךְ בַּחֹ֑מֶץ וַתֵּ֙שֶׁב֙ מִצַּ֣ד
הַקּֽוֹצְרִ֔ים וַיִּצְבָּט־לָ֣הּ קָלִ֔י וַתֹּ֥אכַל וַתִּשְׂבַּ֖ע
And Boaz said unto her at meal-time: ‘Come hither, and eat of the
bread, and dip thy morsel in the vinegar.’ And she sat beside the
reapers; and they reached her parched corn, and she did eat and was
satisfied, and left thereof
The above example, in separating the 2 terms "pat" and "lechem" makes it pretty clear that "pat" means "piece".
I am assuming that when both Mishnah, and in your case your quoting Shulchan Aruch, they use the term "pat" when meaning eating a slice or piece of bread. I think "lechem" would be used when it refers to "bread" as a general food, for example, if they were talking about what grains would be considered "bread".