I thought the reason might be that in modern parlance, innuendo is rarely used to the full extent of its definition (an oblique or allusive remark, typically a suggestive or disparaging one; pg. 730, The Concise Oxford Dictionary, 10th Edition). Rather, in my experience anyway, innuendo is practically always seen in phrase 'sexual innuendo', which Wikipedia defines as follows:
A 'risque' double entendre playing on a possible sexual interpretation of an otherwise innocent uttering
To my mind, 'insinuation' retains a much broader base of application, so sentences like 'Her voice contained the insinuation of guilt' or 'In his extreme politeness was the insinuation that I didn't belong' are perfectly natural. I've never encountered 'innuendo' in such contexts.
However, that theory doesn't bear out on a Google n-gram comparing the occurrence of 'innuendo' and 'sexual innuendo'. Based on what I proposed, one would expect that in recent times, the usage of 'innuendo' and 'sexual innuendo' would be roughly equal, suggesting that 'innuendo' usually appears as part of the phrase 'sexual innuendo' or that 'innuendo' would only just exceed 'sexual innuendo', suggesting occasional use of 'innuendo' in other contexts. Instead, this is what I got:
Shocker: 'innuendo' is five times as common as 'sexual innuendo'...
Although, it would seem that of the two, only 'innuendo' can be sexual. The phrase 'sexual insinuation' practically doesn't exist, or at least, so says Google Ngram Viewer. So maybe that's the difference between the two you're looking for
That being said, I look forward to a more solid answer, if such can be provided. I just gave my thoughts to get the ball rolling.