I wrote a fourteen-line poem in iambic pentameter consisting of two rhyming couplets followed by ten lines of blank verse. Would it be accurate to call this a sonnet?
No, that wouldn't be a sonnet. A sonnet needs to have a given number of lines per verse. Italian sonnet goes 4-4-3-3; English sonnet goes 4-4-4-2. Rhyme scheme varies (abab or abba, for instance). I've never heard of an unrhymed sonnet, and it goes against the idea of a sonnet being a "little song" (that's what the name means). In any case, the verse structure is non-negotiable; 4-10 isn't an option.
YES! There are many different kinds of sonnet.
What most people do not know is that a sonnet does not even need to necessarily have 14 lines. Yes! Dante Alighieri e.g. has many sonnets with 22 lines (called "Sonetto rinterzato"). There are many many variations of the sonnet; it just happened that the rhymed 14 lines one was preferred over the others through time (which is a pity, right?) It is not the case with the blank sonnet, which has been practiced by many poets, including you, it seems.
But what, after all, defines a sonnet? What is its essence, if not having 14 lines with a certain rhyme scheme? In Provençal poetry, there was a genre of poetry named Son, which in Italy was called Canzone, and translates to "Song"; it is a long poem made by many stanzas: these stanzas did not have a fixed form, but there were some rules. These rules are explained in Dante's De Vulgari Eloquentia. A stanza is divided into two parts: a front and a coda. These parts may contain a non-fixed number of lines, as long as the rhyme scheme differs between them, as well as the syntactical rhythm, double or triple: i.e., if the front consists of one quatrains, the coda must contain one triplet, each with a different rhyme scheme. Why such? Because poetry was accompanied by music, and each part, front and coda, means a different melody, that is re-sung at each new stanza; the difference in rhythm and in rhyme scheme accentuates this contrast between parts.
Now, imagine you have this son, whose stanzas are made of a front with two quatrains and a coda with two triplets. The first guy who wrote only one stanza of Son, and thought it was enough, invented the Son-net, the little Son.
So at its core, the sonnet is not even a fixed form. Its essence is contrast between two parts, which is assigned by the volta.
An English sonnet generally does follow one of a number of established rhyme schemes. But I've encountered many modern 14-line unrhymed poems which could reasonably be thought of, and sometimes presented by their authors as, sonnets. (Of course, I'm sitting on a beach as I write this, and is there a good poetry library nearby in which to find supporting references; is there heck!)
I think that the more important feature of a sonnet, than its rhyme scheme, is that there is a 'turn' in theme (or subject or mood or ...) between the first eight lines and the final six.