What's the linguistic relation between
the Turkic words bin or min and Latin word mille meaning thousand
Turkic dil and dutch taal meaninge language?
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There is no known linguistic relation. For (unprovable) ideas about a relationship, cf. http://en.wikipedia.org/wiki/Eurasiatic_languages.
There are three reasons that words in different languages may sound similar:
Common origin gives us series of related words. For instance, English "father" and Latin "pater" have a common origin. But then we have a whole series of words that have a similar fonetic structure in Germanic languages and other Indo-European languages, particularly featuring the peculiarity that what begins in "f" in Germanic languages begins in "p" in non-Germanic languages, and what sounds as "th" in English sounds as t in other languages.
So we have,
father (English) - Vater (German) - pater (Latin)
mother (English) - mater (Latin)
fish (English) - Fisch (German) - pisces (Latin)
foot (English) - Fuss (German) - podos (Greek)
feather (English) - pteros (Greek)
When we do not have those series, then a common origin cannot be established. In the particular case you cite, we do not have any consistent series of words in which Turkish initial /b/ corresponds to Latin initial /m/, nor Turkish final /n/ to Latin final /l/. This means that the similarity is very probably - quite certainly, indeed - not due to a common origin (or is rooted in a common origin so ancient that it has left no real trace in either language).
This leaves us with the hypotheses of 2. loans, and 3. coincidence. In the cases you bring into our attention, a loan is also quite unlikely. Words for "language" are quite central vocabulary in any language, which will not have much reason to borrow it. You borrow words like "spaghetti", that denote objects that you didn't know previously to an inter-cultural contact; and if you borrow a word like "language", it usually is an erudite borrowing, to establish a more refined/abstract connotation than the original "tongue". Neither Latin nor Turkish seem to have any problems with /b/ or /m/, so if they had borrowed from each other, both words would start with /b/ or both words would start with /m/.
So, the most likely is that this is a coincidence, that you notice because of the similarity in meaning. But similarity in meaning is elusive; in the examples above I cited "feather" and "pteros" as related words - which they are, albeit their meaning being quite different. If there isn't historic evidence of a borrowing, or comparable series of words that can establish a common origin, coincidence is by far the most likely explanation for such irregular similarities.