I wrote:
"When a third capacitor is added in series with the inductor, then it becomes a Clapp oscillator."
No. A clapp oscillator has a completely different topology, non-inverting amplifier versus inveting amplifier with colpitts oscillator.
Here are several sources in line with my statement.
From:
http://en.wikipedia.org/wiki/Clapp_oscillator
"The Clapp oscillator is a Colpitts oscillator that has an additional capacitor placed in series with the inductor."
From:
**broken link removed**
"The Clapp oscillator is distinguished from the Colpitts oscillator by the addition of C0 in series with L."
From:
"The Clapp oscillator is simply a Colpitts oscillator with an extra capacitor in series with the coil."
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The above could be called a generalization, of course. It doesn't have to mean that any and every Colpitts type can be turned into a Clapp type
From collecting Colpitts and Clapp oscillator schematics, I find there are many variations. These are different depending on the placement of the LCC tank. (How it is fed and at what moments in the cycle, what components it connects to, whether the supply is in the loop, etc.)
So you could be correct, in the sense that not every Colpitts variation may be adaptable to being turned into a Clapp type.
Example, a transistor which needs DC bias current. If that current comes through the coil, then it will not work if we put in a series capacitor. It will block DC current.