These are the exact same word, and yes both mean "world" but no you cannot substitute them for each other.
What is the meaning of Mundum?
: against the world : in defiance of all general opinion.
What is the Latin name of Mundi?
Mundi- Sphaeranthus indicus is used in Ayurvedic treatment of pain, localized swelling, indigestion, headache, cough, elephantiasis, goiter, skin diseases and to improve the sexual vigor. Latin Name- Sphaeranthus indicus Linn.
What is the origin of the word Mundi?
anima mundi (n.)
From fem. of Latin animus "the rational soul; life; the mental powers, intelligence" (see animus) + genitive of mundus "universe, world" (see mundane).