I have a transcriptome data of 10.8gb R1.fastq and R2.fastq each. I then compressed these pairs using `gzip R1.fastq` and `gzip R2.fast2`, and now the files are 2.2gb and 2.4gb. Is it possible for two compressed files to have different size when the uncompressed files are of same size?
Yes.  It's perfectly possible, even if the reads are the same length.  One might have sequences that are a little more repetitive, and therefore more compressible.  If they have the same number of lines, that's all that matters.

It of course also possible to run gzip with different levels of compression, but you don't seem to have done that. in this case.