The justification for RAND_pseudo_bytes is somewhat dubious, and the reality
is that it is frequently being misused. RAND_bytes and RAND_pseudo_bytes in
the default implementation both end up calling ssleay_rand_bytes. Both may
return -1 in an error condition. If there is insufficient entropy then
both will return 0, but RAND_bytes will additionally add an error to the
error queue. They both return 1 on success.
Therefore the fundamental difference between the two is that one will add an
error to the error queue with insufficient entory whilst the other will not.
Frequently there are constructions of this form:

if(RAND_pseudo_bytes(...) <= 1)
	goto err;

In the above form insufficient entropy is treated as an error anyway, so
RAND_bytes is probably the better form to use.

This form is also seen:
if(!RAND_pseudo_bytes(...))
	goto err;

This is technically not correct at all since a -1 return value is
incorrectly handled - but this form will also treat insufficient entropy as
a...