To definitively answer this question, one would need to know the Bible verses being compared...
"Jehovah God" almost certainly refers to יְהוָ֥ה אֱלֹהִ֖ים "YHWH elohim". It is combination of the proper name of God (YHWH, known as the Tetragramaton; rendered in English as Yahweh or Jehovah, but the vocalization is uncertain - see below) and the generic word for god (usually). The convention followed by most translations is to render the hyphenated "YHWH elohim" as "LORD God" (all caps).
"The Lord" is usually a translation of אֲדֹנָי "Adonai". It is a special plural form of adon, which means lord or master, used only in reference to God. The reason that it is plural is because the Hebrew word for God is grammatically plural and Adonai was often substituted for YHWH and/or elohim out of respect for the divine name. (Eventually Hebrews stopped pronouning the divine name out loud at all). The convention followed by most English translations is to render Adonai as "The Lord" (with only the letter "L" capitalized).
So, the difference between "Jehovah God" and "The Lord" is a lot like the difference between saying "Barack Obama" (name) and "The President" (title). Both are frequently used in the Old Testament, among dozens of other names and titles, to describe (the only) God of the Hebrews.
The English word for YHWH is Yahweh or Jehovah. Because the Israelite stopped saying the name aloud before the third century BC and vocalization (vowels) were not added to the written text until the first millennium AD (finalized in the 9th century), the correct vocalization is uncertain. The Masoretic (9th century) vowel points suggest Yəhō'wāh, but the word is variously also pronouned yä′wā*, -wĕ; Yah·veh (-vā, -vĕ); Jah·veh (yä′vā, -vĕ); Jah·weh (yä′wā, -wĕ). YHWH with or without conjunction with the various titles for God occurs more than 6000 times in the Hebrew Bible.
Yahweh is occasionally shortened to Jah or Yah (Hebrew: יהּ Yahu). The short form of the name occurs 50 times in the Hebrew Bible, of which 24 form part of the phrase Hallelu-jah. Adonai occurs about 450 times.
By the way (and to complicate things even more!), the Hebrew equivalent of the English letter "J" is pronounced as a "Y" in Hebrew, so that the name Jacob, for example, is pronounced Yӓʹ-kōb in Hebrew.