There is a lot of overlap, which is why Torm is Lawful Good, while Helm is Lawful Neutral.
Torm is a god of Honor, but most importantly duty - whatever form that duty may take. A Tormish will not accept just any duty someone asks to charge them with -- they must consider carefully what the thing is they are asked to do, and be prepared to follow it to its completion.
Helm is a god of Guardianship. Guardianship is a type of duty, but it carries connotations all its own. A Helmite will more likely accept a task of guardianship than a Tormish will accept a charge that is dubious in purpose. Helm, the god, was known and reviled for years as the god who retained sole powers of divinity, and who guarded the path back to the heavens during the Time of Troubles.
A true guardian will guard whatever he is charged with, even if doing so will cause innocents to come to harm.
In my take, let's propose a hypothetical pairing of two adventurers - a cleric of Helm, and a Paladin of Torm. Both are requested to guard a castle gate, to protect a Cormyrean Noble. This pair has a view of a shallow ravine. Into the ravine approach two orcs, chasing a helpless farmer. The Paladin is far more likely to leave his post to assist the obviously outmatched farmer. The Cleric, however, has been charged with guarding his post, and BY HELM he's not going to give! The paladin, while faced with a tough choice, would be hard pressed to allow an innocent to come to harm while he stood by and watched.
To sum up: Helm is a god of Law, while Torm is a god of Good and Law. Torm is a little more proactive than Helm would be, I think.