Ephrath was linked with Bethlehem
Ephrath appears early in the Bible as a place near Bethlehem. When Rachel died during Jacob's journey through Canaan, Jacob buried her on the way to Ephrath, and the account identifies Ephrath as Bethlehem (Genesis 35:19).
That connection remains important later. Micah speaks of Bethlehem Ephratah as the small town from which a ruler for Israel would come (Micah 5:2). So when Scripture uses Ephrath or Ephratah in this setting, it is closely tied to Bethlehem in Judah.
And Rachel died, and was buried in the way to Ephrath, which is Beth–lehem.
Ruth's family came from Bethlehem
The clearest use comes at the beginning of Ruth. A famine led Elimelech, Naomi, Mahlon, and Chilion to leave Bethlehem in Judah and live in Moab. The writer calls them Ephrathites of Bethlehemjudah, describing where this family belonged (Ruth 1:2).
This isn't the name of a separate religion or a mysterious people group. It is a family and place description. When Naomi returned, Ruth came with her to Bethlehem. Ruth later married Boaz, and their son Obed became the grandfather of David (Ruth 4:13-17).
And the name of the man was Elimelech, and the name of his wife Naomi, and the name of his two sons Mahlon and Chilion, Ephrathites of Beth–lehem–judah. And they came into the country of Moab, and continued there.
Why another setting can sound different
The word can be confusing because Elkanah, Samuel's father, is called an Ephrathite in a sentence that places his home in the hill country of Ephraim (1 Samuel 1:1). In that context, many readers understand the description as relating to Ephraim or its region, rather than to Bethlehem in Judah.
Yet Chronicles traces Samuel's family through Kohath, one of Levi's sons (1 Chronicles 6:22-28). That means a regional description need not settle a person's tribal ancestry. People could be identified by the area where they lived as well as by their wider family line.
Now there was a certain man of Ramathaim–zophim, of mount Ephraim, and his name was Elkanah, the son of Jeroham, the son of Elihu, the son of Tohu, the son of Zuph, an Ephrathite:
Read the name in context
Jeroboam is also called an Ephrathite. The verse names him as being of Zeredah and identifies his mother as Zeruah, a widow (1 Kings 11:26). It does not need to mean precisely the same thing as Ruth's Bethlehem connection.
So, in Ruth, Ephrathites clearly refers to people of Bethlehem Ephratah. In accounts set around Ephraim, the term may carry an Ephraim-related sense. Place names and family labels in the Bible often overlap. Reading the whole sentence, and the story around it, usually makes the intended meaning clearer.