Marital relates to marriage — marital status, marital problems. Martial relates to war or the military — martial arts, martial law. The letters are simply transposed, which is why typing one for the other produces a sentence that passes spellcheck and reads very oddly.
The core difference
Two unrelated words separated by a letter swap.
- marital — of marriage: marital status.
- martial — of war: martial law, martial arts.
Why spellcheck cannot help
Both are real words, so the swap produces something grammatical. "Martial status" on a form and "marital law" in a news report are the classic results, and both have reached print more than once.
The roots
Marital is from Latin maritus, husband. Martial is from Mars, the Roman god of war — the same source as the planet and the month of March, which was named for the start of the campaigning season.