As adjectives the difference between doomed and bound
is that
doomed is certain to suffer death, failure, or a similarly negative outcome while
bound is (with infinitive) obliged (to) or
bound can be (obsolete) ready, prepared.
As verbs the difference between doomed and bound
is that
doomed is (
doom) while
bound is (
bind) or
bound can be to surround a territory or other geographical entity or
bound can be to leap, move by jumping.
As a noun bound is
(often|used in plural) a boundary, the border which one must cross in order to enter or leave a territory or
bound can be a sizeable jump, great leap.