Regarding the difference between cDNA library and RNA sequencing (Biochem. technique)
The construction of a cDNA library involves making a DNA 'copy' of the mRNA because the aim is to synthesise a large set of recombinant plasmid molecules, each containing a different cDNA and each propagated in E. coli.

The heyday of cDNA library construction predates the invention of PCR. 

The key difference between the two approaches that you are comparing is that one (cDNA library) involves creation of a physical representation of the expressed genome whereas the other is an informational representation.