Let us take the word "love" in the New Testament. The passage in John 21 shows a remarkable difference. I have copied the passage and inserted the Greek numbers for all forms of "love."
15 So when they had dined, Jesus saith to Simon Peter, Simon, son of Jonas, lovest (G-25) thou me more than these? He saith unto him, Yea, Lord; thou knowest that I love (G-5368) thee. He saith unto him, Feed my lambs.
16 He saith to him again the second time, Simon, son of Jonas, lovest (G-25) thou me? He saith unto him, Yea, Lord; thou knowest that I love (G-5368) thee. He saith unto him, Feed my sheep.
17 He saith unto him the third time, Simon, son of Jonas, lovest (G-5368) thou me? Peter was grieved because he said unto him the third time, Lovest (G-5368)thou me? And he said unto him, Lord, thou knowest all things; thou knowest that I love (G-5368) thee. Jesus saith unto him, Feed my sheep.
In the back of the Strong's concordance is a Hebrew dictionary and Greek dictionary. Be sure to flip to the correct one! For the above passage, we will find the Greek numbers 25 and 5368.
Here is what we discover:
25 agapao (ag-ap-ah'-o); perhaps from agan (much) [or compare OT:5689]; to love (in a social or moral sense):
5368 phileo (fil-eh'-o); from NT:5384; to be a friend to (fond of [an individual or an object]), i.e. have affection for (denoting personal attachment, as a matter of sentiment or feeling; while NT:25 is wider, embracing especially the judgment and the deliberate assent of the will as a matter of principle, duty and propriety: the two thus stand related very much as NT:2309 and NT:1014, or as NT:2372 and NT:3563 respectively; the former being chiefly of the heart and the latter of the head); specifically, to kiss (as a mark of tenderness):
From these definitions, we see that Jesus was asking Peter, "Do you really love Me?" and Peter was answering, "Lord, I have an affection for you." The third time, Jesus asked, "Do you have an affection for Me?" and Peter was grieved because he could not claim to really love Christ. Reading the original definitions help shed a deeper understanding on the words.
Topical Study with Hebrew and Greek Words
With the realization of different root words, you can do a study on the individual root words. You can look up all of the verses using agape (G-25) love and then all of the verses using phileo (G-5368) love and follow the pattern of a normal topical study.