The easiest way to look at it...

Crisis on Infinite Earths gave Lois and Clark two babies, where before they only had one. Nothing was indicated after that on the status of those babies. Superman and Lois has their sons in their teenage years, which places this series 10 to 15 years after the end of Supergirl. That is the reason why they can do so much with it and not be interfered by any of the previous shows.