MATLAB model of an op-amp's Open Loop Gain
Let's look at the open loop gain plot from the datasheet you linked.



The 3-dB frequency is where the gain drops by 3 dB from the DC value, which I circled (roughly) in red.

The GBW is where the gain drops to 0 dB, which I circled in blue.

You can see the 3-db frequency is about 200-250 kHz, pretty close to what you calculated.

The GBW product, according to this chart is about 300 MHz, which is somewhat more than the 230 MHz given in the characteristic tables. This is likely due to some slight discrepency in operating conditions between the measurement used to determine the value in the table and the one used to generate the plot.


  The datasheet gives a value of 500 MHz for both of them, but the figure in the datasheet seems to extend beyond past that.


I'm not sure what you mean here.

I see a spec in the datasheet that give 500 MHz typical for the bandwidth in gain-of-1 configuration. This is higher than the 230 MHz GBW product due to peaking in the response when configured for gain of 1, as shown in Figure 1: