They're similar but distinct concepts. Negligible senescence means after a point aging doesn't negatively affect the organism. They don't lose reproductive capability or experience functional decline. Imagine being 20 forever.
Biological immortality means after some point mortality rates don't increase with age - you can still grow old, it just won't directly kill you. Biologically immortal organisms don't have a max lifespan, if they're lucky they can just keep on going, but they may be dramatically more feeble than their younger counterparts.
I think some Lobsters and Crocodiles are in the later category. Immune to cancer, their cells divide without limit over the years. So they never stop growing. The enormous ones are the oldest, and have a size fitness advantage in hunting and other combat, but a counter balancing fitness disadvantage in their increased needs.
Biological immortality means after some point mortality rates don't increase with age - you can still grow old, it just won't directly kill you. Biologically immortal organisms don't have a max lifespan, if they're lucky they can just keep on going, but they may be dramatically more feeble than their younger counterparts.