diode current ratings
Average current rating is less than the continuous rating because the diode forward voltage changes with current, and dissipation is higher at higher current, so for a presumed sinusoidal waveform the dissipation will be higher than for the same average DC current. 

So if you are passing DC through the diode, you use the continuous rating. If you are using it as a rectifier you use the average rating. 

Note that those BAV99 ratings are given at an ambient temperature of 25°C so for any practical application you're going to be limited to much less than those ratings. You have to dig into the mounting, the junction-to-ambient thermal resistance and consider the heating from both diodes if applicable. 

The 1N400x is rated 1A average at Ta = 75°C so it may be a practically useful rating, depending in the application. 

There are other major differences- while both could be used for mains frequency rectifier applications, the 1N400x is far more rugged, but very, very slow, causing more hash (EMI) and making it useless for higher frequency applications.