The Colpitts oscillator is a time-tested design — from 1918. [The Offset Volt] has a few videos covering the design of these circuits including an op-amp and a transistor version. You can find the videos below.
You can tell a Colpitts oscillator by the two capacitors in the feedback circuit. The capacitors form an effective capacitance for the circuit (assuming you have C1 and C2) of the product of C1 and C2 divided by the sum of the two capacitors. The effective capacitance and the inductance form a bandpass filter that is very sharp at the frequency of interest, allowing the amplifier to build up oscillations at that frequency.
It is unusual to show an op-amp oscillator, and it is interesting to think about the design changes and limitations discussed in the video. The video isn’t just theoretical. He also builds the circuit and looks at the real world performance.
It is also interesting to look at the difference between the op amp and the bipolar circuit. Of course, you can use other active devices like a FET, too. This is also an important circuit when a crystal is part of the feedback circuit instead of an inductor.