What's the Difference Between UQI and SSIM Measures for Image Similarity / Quality?
The developers of both are the same hence the similarity is indeed "By Design".  

The only difference is the addition of 2 constants in SSIM (C1 and C2).

The UQI:



The SSIM:



As the writers write in the SSIM paper:



Namely, UQI is a private case of SSIM for C1 = 0 and C2 = 0.