Linkers differ from adapters because:
Linkers are short double-stranded blunt-ended oligonucleotides containing one or more restriction enzyme recognition sites. They are ligated to blunt-ended DNA fragments and then digested with cognate restriction enzyme to create cohesive ends. Adapters already possess a blunt end and a pre-formed sticky end, so no digestion after ligation is necessary. Thus the distinguishing feature of linkers is requirement for restriction cleavage post-ligation to expose sticky termini, which risks concatemer formation and insert cleavage if internal sites exist, unlike ready-to-use adapter strategy.
Ref: NCERT Biology Class XII Principles on Klenow fill-in labeling, Lehninger Chapter 9 DNA cloning techniques, and Molecular Cloning by Sambrook Chapter 10 documenting end-labeling of cohesive termini.