You have two different fast pwm modes (fast pwm to 255 and fast pwm to 1023).
With the same prescaler, the timer can not count up to 255 and 1023 at the same frequency. You should be seeing frequencies of 62500 and 62500/4 = 16625
With FastPWM you can have either a fixed frequency by the fixed 8/9/10 bit TOP or you can have a variable frequency with any 16 bit TOP value in OCR1A or ICR1.
You are right, 16MHz/1024 is much too low. A controller with a timer frequency of at least 62.5*1024 kHz = 64 MHz is required.
@oliveirah 1. I hope that you know the meaning of "resolution" here in the context of PWM signal. 2. I hope that you know the meaning of "duty cycle" of a PWM signal. 3. If you choose Mode-15, the frequency will be controlled by OCR1A Register and the duty cycle will be controlled by OCR1B Register. The smallest amount of time by which the duty cycle of this single slope Fast PWM signal can be changed (this is called the resolution) is:
62.50 us (10-3/(62500x256)).
4. You can set the following parameters (derived using Fig-2 of post #9) to get 62500 Hz Fast PWM signal at 25% duty cycle in Mode-15.