Am I right and the difference between unceasing and ceaseless (for example, attempts) is that
the first is more likely used when smb. does something – does, does and does - being guide by some his/her internal motives and despite everything :),
whereas the latter is more probably used when there are some external circumstances that make no hope for successful ending for that
Or it’s just my, yet another, cranky thought and wrong listening/understanding, but in your real use of the words there is no (such a) difference?
Optimistically, I thought your question would be easier to tackle in the morning (I know, many mornings have gone by since you actually posed it!). Yet, try as I might, I can’t seem to find a nuance in meaning between both terms, except perhaps that ‘unceasing’ is formal and less frequently used.
Another synonym is ‘incessant’, though this word can have a negative connotation: man’s incessant greed for power and wealth, a baby’s incessant wailing, incessant whining/nagging/traffic noise, etc.
By the way, your definition of ‘unceasing’ could, to some extent, fit that of ‘unyielding’ or ‘relentless’.
Just like to toss in another suggestion concerning these two words. To me ceaseless is the word describing something like a dog’s barking that never stops -I’ve got one two doors away that should be confronted by Vlad the Impaler as soon as possible, preferably tonight.
Unceasing is often used in the sense of unflagging, indefagitable, untiring and is linked with abstract nouns like loyalty, devotion, dedication - aptly describing the attitude of the moderators on this site!