First of all, in English, the word 'new' does mean different and you can use it without hesitation for both.
In programming, to define a new object different from others, they use new Object()
When a baby is born, they say 'new baby'.
When they say 'new approach' they imply both new and different.
Other synonyms of 'new' meaning 'new and different' are
But you should mind the word combinations like 'innovative approach', 'advanced technology'.
Following Pureferret's comment, if we refer to programming, and need a single new and different something, we use 'unique' like 'unique key' in database.
So, at the time something new singular and different appears you can call it 'unique'