You can't have your ships everywhere at once! The regular waves are mostly there afaik, to keep pressure on you. If they exist at all.
But there is also threat & threatfleet who can and will showup if they think they can beat up your planet (turrets attack, thus turrets make you a tougher target for them), CPAs (which will sync with other nasties on higher difficulties to overwhelm your crap), and depending on minor factions and other options, exowaves (several kinds), extra attack spawns (vengeful AI for example), AI champion frigate waves (if you have champions on), random attacks (marauders, hybrids hives, unfriendly roaming enclaves, purple dyson gatlings, dark spire revengeances, astro trains, etc) and that with decent turret setup you don't need to divert from what your fleet is doing just to shoo the wave off your lawn if the turrets and forts can do it for you.