You arose an interesting point: what was the HtH between Borg and Connors at non official events?
talking off memory, Connors won at Montreal 81, Beaver Creek 82, San Francisco 82,BAires 78 while Borg won at Frankfurt 79, WCT Montreal 79, Pepsi 77,78,79 and If I recall properly, Chicago 83
But I am sure there are more non official matches between both that I can´t recall right now.
Here are all their official (in bold) and unofficial matches that I can think of:
1 - November 1973 - Stockholm SF - Borg 6-4 3-6 7-6
2 - August 1974 - Indianapolis F - Connors 5-7 6-3 6-4
3 - September 1975 - US Open SF - Connors 7-5 7-5 7-5
4 - November 1975 - Stockholm SF - Connors 6-2 7-6
5 - February 1976 - Philadelphia F - Connors 7-6 6-4 6-0
6 - March 1976 - Palm Springs SF - Connors 6-4 6-1
7 - September 1976 - US Open F - Connors 6-4 3-6 7-6 6-4
8 - September/October 1976 - Caracas RR - Connors 6-4 5-7 6-3
9 - January 1977 - Pepsi Grand Slam F - Borg 6-4 5-7 6-3
10 - July 1977 - Wimbledon F - Borg 3-6 6-2 6-1 5-7 6-4
11 - January 1978 - Masters F - Connors - 6-4 1-6 6-4
12 - January 1978 - Pepsi Grand Slam F - Borg 7-6 3-6 6-1
13 - April 1978 - Tokyo (Suntory Cup) F - Borg 6-1 6-2
14 - July 1978 - Wimbledon F - Borg 6-2 6-2 6-3
15 - September 1978 - US Open F - Connors 6-4 6-2 6-2
16 - September 1978 - Buenos Aires F - Connors 5-7 6-3 6-3
17 - February 1979 - Pepsi Grand Slam F - Borg 6-2 6-3
18 - April 1979 - Las Vegas F - Borg 6-3 6-2
19 - July 1979 - Wimbledon SF - Borg 6-2 6-3 6-2
20 - November 1979 - Tokyo Indoor F - Borg 6-2 6-2
21 - December 1979 - Frankfurt RR - Borg 6-3 4-6 6-3 6-4
22 - December 1979 - WCT Challenge Cup F - Borg 6-4 6-2 2-6 6-4
23 - January 1980 - Masters RR - Borg 3-6 6-3 7-6
24 - February 1980 - Salisbury RR - Borg 6-3 6-1
25 - March 1980 - Copenhagen SF - Connors 6-4 6-2
26 - January 1981 - Masters SF - Borg 6-4 6-7 6-3
27 - February 1981 - Toronto (Molson Challenge) RR - Connors 7-5 6-3
28 - July 1981 - Wimbledon SF - Borg 0-6 4-6 6-3 6-0 6-4
29 - September 1981 - US Open SF - Borg 6-2 7-5 6-4
30 - July 1982 - Industry Hills F - Connors 5-7 6-2 6-2 6-7 6-2
31 - July 1982 - Richmond - Connors 6-4 3-6 7-5 6-3
32 - September 1982 - Ottawa - Borg 1-6 6-3 6-3 1-6 6-2
33 - October 1982 - Montreal (Molson Challenge) F - Connors 6-4 6-3
34 - November 1982 - Seattle - Connors 6-4 3-6 7-5
35 - November 1982 - Los Angeles - Connors 6-3 2-6 6-2
36 - November 1982 - Vancouver - Connors 6-2 5-7 6-4
37 - November 1982 - San Francisco - Connors 7-5 7-6
38 - January 1983 - Rosemont RR - Borg 6-4 1-6 6-2
39 - February 1983 - Baton Rouge - Connors 6-7 6-4 6-3
40 - February 1983 - Providence - Connors 6-4 6-4
41 - April 1983 - Seoul - Connors 5-7 6-1 4-6 6-4 7-6
42 - April 1983 - Tokyo (Suntory Cup) F - Connors 6-3 6-4
Official h2h: Borg 15-8 Connors
Unofficial h2h: Connors 15-4 Borg
Overall h2h: Connors 23-19 Borg
By season (their matches at the Masters and Rosemont Challenge of Champions belong to the prior years):
1973: Borg 1-0 Connors (0-1)
1974: Connors 1-0 Borg (1-1)
1975: Connors 2-0 Borg (3-1)
1976: Connors 4-0 Borg (7-1)
1977: Borg 2-1 Connors (8-3)
1978: Borg 3-2 Connors (10-6)
1979: Borg 7-0 Connors (10-13)
1980: Borg 2-1 Connors (11-15)
1981: Borg 2-1 Connors (12-17)
1982: Connors 7-2 Borg (19-19)
1983: Connors 4-0 Borg (23-19)