James, No doubt someone else will tell you more in depth, but ill have a go....
When i had a battry cable made up by a local motor factor, the chap that did it asked whether i wanted negative or positive terminals,
he said the difference is in size, ie one is bigger than the other, so if your new battery has say positive terminals and they are say the larger of the sort, And your cables have got negative terminals and are say the smaller type they wont fit as they will be like you say too tight,
I am unsure as to which type is the larger of the two types, but im sur all that is needed is a replacement cable terminal of the correct size to suit and all will be well, Although i could be totaly wrong
Hope this helps
Charlie