Hey Daxiuz-
The grid is only a visual representation of space rather than a physical location. The snapping distance will always snap to the same distance each time it moves (in this case setting snapping distance to 50 will move 50cm each time). To align the points of the spline as you suggest the easiest solutions would be to either (A) select the point and then manually set the value so that it lands on the grid. Doing this will allow you to drag the point along the grid from there. The other option would be to (B) change the snapping distance down to 10 and move the point to one of the bold lines of the grid (every 10 grid markers is slightly more pronounced). After doing that you can set the snapping distance back to 50 and drag the point along the grid.
Cheers