DISCUSSION
Where did our Harrison families originate?
Harrison families have ancient roots in most of the Y-DNA haplogroups identified so far. When the adoption of surnames became popular in the 1300s, many unrelated people became Harrisons as various sons of unrelated men named Henry, Henri, Harry, Harris, and the like became known as Henryson, Harryson, or Harrisson. Eventually by the 1600s most of these came to be spelled "Harrison," although variations still exist. The 1881 UK Census shows the distribution of Harrisons across the British Isles, and most Harrison families were found in northern England. Harrisons were most commonly found in York, Harrogate, Preston, Lincoln, and Derby. The following map shows where Harrisons were most commonly found in the UK in 1881.

How close a match do I need to be considered "related" to another person?
This is an excellent question. FamilytreeDNA has analyzed hundreds of thousands of samples and matches, and has determined that two individuals will either be considered "related," "probably related," or "not related," based on how closely the two peoples' results match. This is complicated a little by the fact that some markers mutate faster than others, so a match of 35 out of 37 markers could still indicate a very close relationship if the two markers that are different are fast changing markers. These charts below adapted from FamilytreeDNA data should help you establish whether you and another Harrison are related based on your test results:
67 Marker Tests:
67/67 Distance of 0 Very tightly related
65/67 or 66/67 Distance of 1 or 2 Tightly related
61/67 to 64/67 Distance of 3 to 6 Related
60/67 Distance of 7 Probably related
58/67 or 59/67 Distance of 8 or 9 Only possibly related
57/67 or less Distance of 10 + Not related
37 Marker Tests:
37/37 Distance of 0 Very tightly related
36/37 Distance of 1 Tightly related
34/37 to 35/37 Distance of 2 to 3 Related
33/37 Distance of 4 Probably related
32/37 Distance of 5 Only possibly related
31/37 or less Distance of 6 + Not related
25 Marker Tests:
25/25 Distance of 0 Related
24/25 Distance of 1 Related
23/25 Distance of 2 Probably related
22/25 Distance of 3 Probably not related
21/25 Distance of 4 Not closely related
20/25 Distance of 5 Not related in last 2000 years
19/25 Distance of 6 Not related in last 5000 years
18/25 or less Distance of 7+ Totally unrelated
12 Marker Tests:
12/12 Distance of 0 Probably Related
11/12 Distance of 1 Possibly related
10/12 Distance of 2 Probably not related
7/12 to 9/12 Distance of 3 to 5 Not closely related
6/12 or less Distance of 6+ Totally Unrelated