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The definitions seem very much alike:

superposed - Place (something) on or above something else, esp. so that they coincide: "superposed triangles".

superimpose - Place or lay (one thing) over another, typically so that both are still evident.

Are they just synonyms?

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2 Answers

They are synonyms but have different scopes of usage.

Superimpose is the term found in general use.

Superpose is used mostly in scientific or mathematical contexts; see 'superposition'.

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Merriam-Webster has them as synonyms, but the difference is this: consider the Star of David, and consider the construction of one with two solid triangles rather than interlocking triangles.

Star of David

The two triangles are superimposed, and both are evident.

Were one triangle not rotated, they would be superposed.

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This is true in mathematics; in geology there is yet another usage, referring to the stratification of layers. –  Mark Beadles Mar 13 '12 at 14:35
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I'm no mathematician, so maybe I'm wrong here, but this seems unlikely to me. In this diagram, the two (implied 3-d) triangles are interlaced, or interwoven. I'd be genuinely surprised if the mathematical usage distinguished between these two words according to visibility from the particular vantage point of the observer. –  FumbleFingers Mar 13 '12 at 15:56
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@FumbleFingers, that is why I said consider the construction of one with two solid triangles rather than interlocking triangles. –  cornbread ninja 麵包忍者 Mar 13 '12 at 16:06
    
I still don't understand. Are you saying that to a mathematician (are you one?) there would be two different ways of arranging the triangles (whether 2-d, 3-d, or "Escherian") such that superimposed/superposed unambiguously distinguishes between the two? –  FumbleFingers Mar 13 '12 at 16:21
    
I am not a mathematician, nor do I play one on television. Yes I am saying that, and the Star of David was the first commonplace geometric structure that came to mind. I have seen Stars of David wherein it is not evident that the triangles interlock, so I wanted to make the distinction, especially after replacing my original (very large) image with an interlocking version. –  cornbread ninja 麵包忍者 Mar 13 '12 at 17:41
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