Answer: Yes there is difference between spiritual initiation and Upanayana.
In spiritual initiation you seek a competent Guru to initiate you in the spiritual path. Every Mantra has inherent power in it. When Guru initiates the disciple this power is transmitted too. That qualified Guru gives you a fully charged divine Mantra and fixes your chosen deity. It contains “Bija” or seed. Then he gives you certain instructions which will be helpful in spiritual life if followed sincerely. He is the dependable Guru for all your life who initiates you most unselfishly. He prays for the welfare of the disciple and sincerely feels for the progress of the disciple in the spiritual Path. The real Guru welcomes all seekers of Truth, irrespective of caste, creed or religion.
Upanayana is one of the Samskaras in the life of a person. Father performs Upanayanam Ceremony and gives Gayatri Mantra. The Gayatri also can lead to the goal, provided it is practiced sincerely.
Even if you are initiated with a Mantra (what you call spiritual initiation) the chanting of Gayatri can be continued.
Try sincerely to progress in spiritual path.