You should look at the read names (samtools view bam_file, column 1) to see if they follow Illumina naming convention. Post a couple of lines (samtools view bam_file | head -2) if you want us to look. It may also be useful to look in BAM header to see if the aligner command line is embedded there. File names may give some clue, if the data is Illumina.
If the read lengths (column 10 in SAM/BAM file) are 300 bp or less they are likely to be Illumina (there is no guarantee, other sequencers will produce reads in this range)
Using grep with binary BAM file will not produce any result other than a note that it encountered a binary file.
Thank you for your input! This is the output of "samtools view bam_file | head -2"
Those identifiers are Illumina with something appended at end
_eR1j
of each read ID. This data came from a HiSeq 3000/4000 sequencer.