Doesn’t the worship of any deity mean one and the same thing?

No, it cannot be taken as the same thing. However, those who think it as the same thing give arguments in favor of it. They are true so far as the worships related to Niranjan are concerned. The Sagun worship is related to Niranjan and the same is true in case of Nirgun worship as well.
Niranjan had three sons—Brahma, Vishnu and Mahesh. Then there were the branches as well as the sub branches that made the whole of Brahmand. As such, the worship of those other than Niranjan himself, also falls within the limit of Niranjan. As the whole of universe has been created by Niranjan, so all kinds of worship being practiced here are related to him at levels.
At all the places- scriptures he has talked about himself and his structures alone. The secret related to Param Purush and Amarlok are consealed and not revealed in any Religious Scripture. After departure from the world, every Jiva reaches the deity he worshiped. For instance, the worshipper of Shiv Ji reaches Shiv Lok, the worshiper of Pitars reaches ancester Lok and the like.
Nevertheless, one should understand that at the time of great dissolution, the worshipers of both Sagun as well as the Nirgun – will reach Niranjan. Even other deities will get absorbed in him. However, the worshipers of Satguru will escape from Niranjan's grip and will attain Amarlok, whether such a thing happens in their life time (Jeevan Mukta) or after their departure from the world.

Mann He Niranjan, Mann He Onkaar, Mann He Hai Kartara.  
Jeev Ke Sang Mann Kaal Rahai, Agyani Narr Jaanat Nahin.  

Mind himself is Niranjan, Mind himself is Onkaar, Mind himself is the Ruling Power of the Universe .The Lord of Death of every being resides with him but ignorant human being is not at all aware of this truth.