By way of supplementing and extending the answers already provided for this question:
As noted elsewhere in this Q&A, the kingdom that was united under the thrones of Saul, David, and Solomon, split in the aftermath of Solomon's reign into distinct "nations": one in the north, and one in the south (narrated in 1 Kings 12). When the two designations "Israel" and "Judah" are used in the deliberate and connected fashion as in the OP's verse, Jeremiah 30:4, it is showing a self-conscious awareness of and attention to these independent political entities.
As also noted, there is a wider pattern of designations used in the Hebrew Bible to refer to these two states:
+---+----------+---------+-----------+
| | Aspect | North | South |
+---+----------+---------+-----------+
| 1 | National | Israel | Judah |
| 2 | Tribal | Ephraim | Judah |
| 3 | City | Samaria | Jerusalem |
| 4 | Mountain | Ephraim | Zion |
+---+----------+---------+-----------+
Examples1
- National: 2 Samuel 5:5: "In Hebron he [i.e., David] reigned over Judah seven years and six months; and in Jerusalem he reigned thirty and three years over all Israel and Judah. Distinguishing the successive phases of David's period of reign over south, and north-and-south, respectively.
- Tribal: Isaiah 11:13: "The envy also of Ephraim shall depart, and they that harass Judah shall be cut off; Ephraim shall not envy Judah, and Judah shall not vex Ephraim. " In Isaiah's vision of a utopian future age, north and south, here designated according to their leading tribes, will be at peace.
- City: Isaiah 10:11: "Shall I not, as I have done unto Samaria and her idols, so do to Jerusalem and her idols?" From Isaiah's "woe" oracles, aligning the capital of the north and south.
- Mountain: Jeremiah 31:6: "For there shall be a day, that the watchmen shall call upon the mount Ephraim: arise ye, and let us go up to Zion, unto the LORD our God." One of the few times in the Hebrew Bible that "(Mount) Ephraim" and "Zion" appear together in a single verse, although separately they occur many, many times.
Tracing these pairs through the HB/OT can illuminate both the nature of the divisions (as in ##1 and 3, above), and the hopes and aspirations that this difference should ultimately be overcome (as in ##2 and 4, above -- see also, e.g., Jer. 50:4-5; Ezekiel 37:15-23).
1 The translation cited is the 1917 JPS translation from Mechon Mamre.