From the title of your post and your question, it seems you want to create a line from points along each stream profile and get the distance between consecutive profile points (vertices along the profile line). Is that correct?
If you have ArcGIS 10 and Arcinfo license, you can try the following:
1. Assuming your points along each stream profile has a unique ID or field value, run the Points To Line tool with the profile ID as the Line Field. You will get a polyline for each stream profile.
2. Run the Split Line At Vertices tool to get lines between vertices. The Shape_length values of the split lines would be the distances you are looking for?
Regards,