Two different polite forms of the conditional conjugation I've noticed some dictionaries give two different results for the polite form of the conditional form, I'll use the verb for example. I am familiar with but not with . Some dictionaries give just one, others give both. Is there a difference in these two in anyway? Are both frequently used?

Neither is common. In fact, and are almost _never_ used in modern Japanese. You have to use .

* I sometimes hear stereotyped samurai in samurai dramas say . It's indeed "if (someone) fights" said in a polite way. It's "stereotyped samurai-ish speech", but I don't know whether old people actually talked like this. People never use it today except as a joke.
* is occasionally found in archaic Japanese documents, Bible translations, hymn books, and so on. But actually it's followed by .
* , , , etc. should be extremely rare, and I would say it's nearly wrong (but apparently a few people seem to use ...). If used, it would leave a very literary, archaic, and/or odd impression.