Why do AM radio stations have secondary frequencies?
The secondary frequency most likely comes from a different transmitter transmitting the same service to a different part of the country. One is probably much stronger than another where you are : move to the other location and you'd get better reception from the other.
This page announces some of the changes in frequencies that are happening (UK). For example you might have found Radio Cornwall on 630 and 657kHz (but not 675kHz) : those channels are closing this year (maybe already have).
There is an incomplete list on Wikipedia : showing the above frequencies as Redruth and Bodmin (both towns in Cornwall) : oddly there are no entries for 675 kHz. It doesn't show any common broadcasts on 549 (Spirit Radio from Ireland?) and 729 kHz however.
They are all multiples of 9 kHz as this is the international standard channel spacing for (LW and MW) AM bands, except in N.America which uses 10kHz.
This also happens a lot on the Short Wave broadcast bands where you will hear e.g. BBC World Service on several bands at once, allowing you to choose whichever band has good propagation to your area at the moment, given the problems of fading and interference especially at night.
Here's a site showing who is on 630 kHz. Click on any other frequency there to see who's on that frequency. I don't know how complete it is.