Meaning of these two words uncertain. They designate a kind of oracle; cf. Num. 27.21.
Septuagint Exodus 28
23 And Aaron shall take the names of the children of Israel, on the oracle of judgment on his breast; a memorial before God for him as he goes into the sanctuary. 24 And thou shalt put the fringes on the oracle of judgment; thou shalt put the wreaths on both sides of the oracle, 25 and thou shalt put the two circlets on both the shoulders of the ephod in front. 26 And thou shalt put the Manifestation and the Truth on the oracle of judgment; and it shall be on the breast of Aaron, when he goes into the holy place before the Lord; and Aaron shall bear the judgments of the children of Israel on his breast before the Lord continually.
Vulgate Exodus 28:30
And thou shalt put in the rational of judgment doctrine and truth, which shall be on Aaron's breast, when he shall go in before the Lord: and he shall bear the judgment of the children of Israel on his breast, in the sight of the Lord always.
When the former prophets died, the Urim and Thummim ceased. The Urim and Thummim were two oracular stones that the high priest would carry in his breastplate. When the Israelites had questions they would ask the Urim and Thummim (see Exodus 28:30). The Urim and Thummim were in use only during the First Temple period. When the prophets of the First Temple died out, the Urim and Thummim ceased.
And thou shalt put upon the breastplate of judgment the Uraia, which illuminate their words, and manifest the hidden things of the house of Israel, and the Tumaia, which fulfil (or perfect) their work to the high priest, who seeketh instruction by them before the Lord; because in them is engraven and expressed the Great and Holy Name by which were created the three hundred and ten worlds, and which was engraven and expressed in the foundation stone wherewith the Lord of the world sealed up the mouth of the great deep at the beginning. Whosoever remembereth that holy name in the hour of necessity shall be delivered. And they shall be upon Aharon's heart in the time that he entereth before the Lord; and Aharon shall bear the judgment of the sons of Israel before the Lord continually.
משה נתנם בחשן בשעת לבישה, א"כ לא היו קבועים בחשן, א"כ היה הכהן משתמש בהם לפרקים ומוציאם מתוך החשן, ואולי היו כ"ב אותיות חקוקות על כ"ב תחיכות קטנות של עץ או של מתכת, והיה הכהן מרים משם אות אחת ואח"כ אות אחרת, והשגחת ה' היתה מזמנת לו תשובה נכונה לשאלתו...ומזה נמשכת קבלת רז"ל שמאותיות שמות השבטים היו מבינים התשובה.
Seeing as Moshe placed these in the Hoshen when it was being worn, as such they were not set in the Hoshen, as such, the Kohen would use them at times and take them out of the Hoshen. Maybe they were 22 letters written on 22 small pieces of wood or metal, and the Kohen would remove them letter by letter, and Divine Providence would give a proper answer to the question. This is where Chazal derived that from the names of the shevatim would the answers be known.
ונתת אל חושן המשפט את האורים ואת התומים סבר רבי אברהם להתחכם בענין האורים והתומים, ואמר (בפסוק ו) כי הם מעשה אומן כסף וזהב, והאריך בענינם כי חשב שהם על הצורות שיעשו בעלי הכוכבים לדעת מחשבת השואל. ולא אמר כלום. אבל הם כדברי רש''י, כתב שם המפורש (תיב''ע) נתון בין כפלי החשן
...אבל הם סוד מסור למשה מפי הגבורה...והענין הוא, כי היו שמות קדושים, מכחם יאירו האותיות מאבני החשן אל עיני הכהן השואל במשפטם ... וזאת מדרגה ממדרגת רוח הקדש, היא למטה מן הנבואה, ולמעלה מבת קול שמשתמשים בה בבית שני לאחר שפסקה הנבואה ופסקו אורים ותומים כמו שהזכירו רבותינו (שם כא:): ואפשר שאחרי שנתן משה בחשן השמות הקדושים של האורים והתומים היו נודעים במסורת ממנו לגדולי חכמי ישראל שמסרם להם עם סתרי תורה...
Rabbi Avraham has thought toward wisdom as regards the Urim and Tummim, and said they were the work of gold and silversmiths, and explained in length that he thought they were the type of shapes made by those who know the stars, to know as the one who asks wishes. He has said nothing. they are as Rashi says, that it was the Divine Name...a secret given to Moshe...and the matter is that these Holy Names, from their power, would illuminate the letters on the stones of the Hoshen towards the Kohen, before he who asked their matter. And this is a level of Ruach HaKodesh, below prophecy but above a Bat Kol, which was heard in Bayit Sheni, after the Nevuah was gone...and after Moshe put the Holy Names in the choshen, they were known through tradition from him to those who knew much in Israel, and gave them over with other secrets of the Torah...