Files ending in .gz are compressed (zipped) files.
The fastq.gz format is a compressed version of a fastq dataset.
The fastqsanger.gz format is a compressed version of the fastqsanger datatype, etc.
Compression saves space (and therefore your quota).
Tools can accept the compressed versions of input files
Make sure the datatype (compressed or uncompressed) is correct for your files, or it may cause tool errors.