I size my ammo so it fits in all my rifles. Some have tighter chambers than others.
Without measuring equipment, you really don’t know what is going on, and suggestions that one rifle has a longer chamber, or a shorter chamber, could be right, or could be wrong. You need to measure these things.
I recommend purchasing a cartridge headspace gage. You can drop a fired case into a gage and see/measure the differences between cases fired in different chambers. If you see that cases that come out of the Savage are too long, than you know what the problem is.
It is also possible that your Lee full length sizing die is not sizing the cases down sufficient to enter the chamber of your other rifle.
The instructions that come with sizing dies generally say something like “turn the die until it hits the shell holder and add a quarter turn”. This is hit and miss, and once you have gages to measure what is going on, you will realize that this poor advice.
I full length size my cases to gage minimum. That works for all correctly headspaced rifles.
There is one other possibility, something that cartridge headspace gages don’t measure, and that is case “fatness”. Cartridge headspace gages are cut large between the base and the shoulder so you can drop fired cases in the gage. I have reamer cut gages, gages that were barrel stubs, and the gunsmith reamed them to depth with the same reamer he used to cut the chamber in the barrel he installed. This gage is therefore dimensionally correct length and width.
In this photo, I had sized this case with this Lee full length sizing die. The sized case will not drop in the reamer cut gage. And that is because this case, even after being sized, is still too fat.
I use small base dies for every caliber I can get them in. Small base dies are more likely to reduce cases to below chamber dimensions than standard full length sizing dies. However, you must set up the die with a cartridge headspace gage or you will oversize the case.