Interesting!
Tammy, I'd like to hear more about your two friends.
I am not very much sure about the naming used. What I have heard and read is that a soul-mate is someone who had incarnated with you in almost all incarnations and have been working together with you in the spiritual evolution of both. This is the first time I heard the word "twin flame". As I understand from your description, twin flames are separate incarnations of the same soul, for wider experience, during the same period of time, be it relative or not. And "sometimes only one of the two people will recognize the soul mate connection because the other does not want to recognize the connection and may be afraid of the intimacy" may very well be correct, as I feel.
These, I picked from the book "A Message of Love":
The longing for the twin soul is well known. When evolution is complete, which means that all the beads on the thread have incarnated and returned, the two strands or stems will become one again. During incarnation, until that is possible, a flower from one stem or a bead from one strand may meet with a flower or bead from its twin essence, but twin souls do not always incarnate at the same time.
There have been periods in your history where it was more common for twin souls to meet, such as in Atlantean, Egyptian, Grecian or Native American Indian incarnations. In the present time a lot of work is often taken on during the course of one incarnation and this means that meeting with twin souls is discouraged by the karmic advisers and helpers. The danger is that the two beings may be so absorbed in each other that the degree to which they move forward their learning process is lessened. When the changes have taken place it will be usual for twin souls to be working together in incarnation once more. Now, the range of available experience is very great and twin souls must live separately in order to cover as much ground as possible.
This is what Gildas, the discarnate guide of Ruth White, the author of the book, says. I shall put the book details in the Books board if it is not already there. The book was very interesting to me....
Love and Light
Dew .