Samtools depth is using the mpileup algorithm to find overlapping data, along with all the nuances that involves. That means filtering by flags (unmapped data, secondary reads, duplicates, QC failure), limits of maximum depth, possibly some other things like removal of overlapping templates (I cannot recall if that is on or off by default), and definitions of what actually means aligned (CIGAR N operation isn't for example; I forget if D is). Note unmapped data here will mean placed (having CHR/POS) but not aligned.

View however is just an unfiltered count unless you also modify the filtering options, and even then it will be counting records spanning the region with N (and perhaps D) cigar ops.

Which is appropriate for you depends on the question you are asking.