Nitrifying bacteria usually go through this sort of growth pattern:
When ammonia is present the first population of bacteria grow. They usually grow pretty fast. They turn ammonia into nitrite. If there is not a continuous source of ammonia they will then die out to match whatever level of ammonia is there.
Ammonia is mostly from protein, for example, from fish food. Fish digest it and produce ammonia as a waste from their gills. Decomposing food, fish waste, fallen leaves, and organic matter in the substrate are other common sources.
Once that first population of bacteria gets going producing nitrite the second population can start to grow. This group includes the species Nitrospira. They turn nitrite into nitrate. Mostly they are slower growing, so a common pattern is that the ammonia disappears, but nitrite spikes, and nitrate slowly climbs.
If there is a lot of ammonia then there will be a lot of nitrite. But these bacteria do not grow very well if the nitrite or ammonia are over 5 ppm, so the cycle can seem to stall. However, slowly the nitrate will show up. Good to do a water change if the ammonia or nitrite get to 5 ppm.
Anyway, here is how I would read your tanks:
1) Low ammonia, no nitrite, some nitrate:
Cycle is not complete, or else your test kit is showing you the locked up ammonia from chloramines. My tests can show as much as 1 ppm ammonia from chloramines, locked up by the dechlorinator. Keep up the water changes to keep the ammonia under .25ppm. Use a dechlorinator that locks up ammonia. Use a test kit that is compatible with the dechlor you are using so you know what you are reading.
2) No ammonia (just dropped a few days ago), some nitrite, sky high nitrate:
This tank is really close to being cycled. Add ammonia to test 1 ppm twice a day so you keep feeding the bacteria. After a few days test again. Skip adding ammonia, and test 24 hours after the last addition. If the ammonia and nitrite are both zero, the cycle is done. Keep feeding ammonia until you are ready to add fish. Do as large a water change as needed to get the nitrate as low as possible before adding the fish.