Is there a single word which means " similar but not quite the same"?

The word you are looking for is the adjective tantamount. In modern use, it is always followed by to. Oxford Dictionaries Online gives its meaning as:

Equivalent in seriousness to; virtually the same as

The real OED also historically attests a verb and a noun of that same spelling, but those are no longer used. It also documents rare attributive uses dating through the 19^th century, of which two citations are:

• 1798 Washington Let. Writ. 1893 XIV. 29 ― The President; to whom I have expressed tantamount sentiments in more concise terms.
• 1868 Rogers Pol. Econ. i. (1876) 3 ― A tantamount service should be given in exchange for them.

So in summary, any idea that works out to essentially or virtually the same thing as a second idea is tantamount to that second idea.

While similar (“Having traits or characteristics in common; alike, comparable” - wiktionary) by itself should work, as may related (“Standing in relation or connection”). In addition consider akin (“Allied by nature; similar; partaking of the same properties; of the same kind” - wiktionary), as in “My idea is akin to his”. More figuratively, nodding acquaintance may work, used in its sense “A casual or partial familiarity; a relationship which is not close or fully developed; an inexact understanding” (wiktionary). For example, “My idea is a nodding acquaintance of his”.