In a certain sense,
coming across and running into do share some slight similarity IMO.
Let's say you are traveling in the
Serengeti Safari on a Jeep and from a distance you see a herd of migrating wilder beasts. You can say in your journal " May 3rd, 2000. As we drove across the Safari early morning,
we came cross / ran into .....a herd.." In this context, both imply a sense of unexpectance. However, the real meaning of
running into is you met the herd head-on and subsequently engulfed by the dust storm as they passed you by. Come across on the other hand, they crossed the path of your travel, or encountered their presence briefly. Just my 2 cents....