Are letters of recommendation usually meant to be tailored to a specific programme?

I am hoping to be applying for a PhD programme in the UK in the next few months. I have already asked the appropriate people if they would be up to writing me letters of recommendation and they responded positively and enthusiastically.

Now, I am not fully certain about the exact programmes I'll apply to. I have a few picked out but I'm also looking into a couple others - not really related to my original picks (think research in A vs. research in B by means of A.

Question: should my referees tailor their letters of recommendation to the specific programmes I'll be applying to, or is the convention usually for letters to be more destination-agnostic? Is it ok to ask a letter-writer to make the letter relevant to many degrees or asking for multiple separate letters is the usual practice?