I apologize if you already got this from the other answers, but you requested baby steps, and I didn't see this particular baby step being explained. :-)
Isn't @hsh and %hsh two completely different things?
Yes, @hsh and %hsh by themselves are two different things, except you never had @hsh by itself in your code. You had @hsh{...}, which is, as you surmised, the hash slice syntax. It has an @ in front because it's accessing a list of values, but the variable that it's accessing from is %hsh.
And when I say a list of values, that's exactly what I mean. Hash slice syntax is a convenient way to get access to more than one hash value at a time. It is equivalent to a list of single hash accesses:
# given a hash:
my %hash = (one => 1, two => 2);
# the slice:
print @hash{"one", "two"};
# is equivalent to:
print $hash{"one"}, $hash{"two"};