More exactly, Yu Sung-Ryong (1542-1607) was a friend of Yi Yo-Shin (1542-1580), not a friend of Yi Soon-Shin (1545-1598).
Yi Yo-Shin is an elder brother of YSS. He died at the age of 38, so YSS fostered his children. You saw him in the drama in YSS's youth episodes.
Won Kyun was born in 1540. So he was even older than Yu Sung-Ryong.
About YSS and Won Kyun relation in real history, it seems that YSS didn't hate Commander Won from the debut. Their relation was aggravated during the war. We can glimpse YSS's sentiments toward Won Kyun if we pay attention to the Admiral's references to him in his Diary. We can find the fact that he became less and less respectful to Admiral Won.
YSS often called him without title when he felt bad about Admiral Won. In Chosun period, even in modern Korea among aged men, to call someone's name without title is considered as an impolite act.
This list was made from the Korean translation of the Admiral's diary. Daemado courteously added English translation on it between parenthesis. (Thanks to Daemado !) We share this with you. ;D
* How did YSS call Won Kyun in his Diary ?1592
15 April : Right Commander of Youngnam ("Kyongsang Right Naval Commander")
(* As you know, Youngnam is a synonym of Kyungsang province. Not our dear Lt. Yi Young-Nam, of course.
)
27 August : Navy Commander of Youngnam ("Admiral Won Kyun")
1593
7 February : Won Kyun, Right Commander of Kyungsang ("Admiral Won Kyun")
15 February : Won Kyun ("Won P'Yong-jung")
(cf. "P'yong-jung" is Won Kyun's secondary name -
ja. Oh, did YSS call him with this friendly name? I never see it in my Korean translation version. I cannot make access to the original version written with
hanja, so I cannot verify which one is exact.)
17 February : Right Commander of Youngnam ("Admiral Won Kyun")
22 February : Right Commander of Kyungsang ("Admiral Won Kyun")
23 February : Won Kyun ("Admiral Won Kyun")
28 February : Won Kyun, Commander of Kyungsang ("Kyongsang Commander Admiral Won Kyun")
8 May : Commander ("Navy Commander")
9 May : Commander Won Kyun ("Admiral Won Kyun")
16 June: Right Commander of Kyungsang Navy ("Kyongsang Right Navy Commander Admiral Won Kyun")
6 September : Won Kyun ("Won Kyun ... jabbered all the time with pointless words")
1594
19 January : Won Kyun, Right Commander of Youngnam ("Admiral Won Kyun")
21 February : Won Kyun ("Admiral Won Kyun")
4 March : Won Kyun, Right Commander of Kyungsang ("Admiral Won Kyun")
13 March : Commander Won Kyun ("Admiral Won Kyun")
12 April : Won Kyun, Commander of Kyungsang ("the Kyongsang Commander Won Kyun")
4 June : Won Kyun ("Admiral Won Kyun")
16 July : Won Kyun, Commander of Kyungsang ("the Kyongsang Navy Commander, Won")
1595
10 January : Won Kyun, Commander of Kyungsang ("the Kyongsang Navy Commander")
20 February : Won Kyun ("Admiral Won Kyun")
27 February : Won Kyun ("Won Kyun")
1596
12 March : ¿øÈä Won Hyung ("the mastermind")
22 August (Leap month) : Won Kyun ("Won Kyun, the Army Commander")
1597
27 April : Won Kyun ("Won")
2 May: Won Kyun ("Won")
5 May: Won Kyun ("Admiral Won")
6 May : Èä¹°, Hyung Mul ("the rascal")
7 May : À½ÈäÇÑ ÀÚ, Eum hyung han ja ("the wicked man")
8 May : Won Kyun ("Won, the wicked fellow" and "the wicked Won")
12 May: ¿ø¿µ°¨ Won Young-gam - signifying Lord Won* ("Admiral Won")
(* I guess YSS used this honorific appellation with pejorative connotation.)
20 May: Èä¹°, Hyung Mul ("the wicked man")
28 May : Won ("Won")
17 June : Won Kyun ("Won Kyun")
22 July : Won Kyun ("Won Kyun") - last mention