If you look at the grammar structure closely, there is a difference. Phrases like "in/with regards to" are in the common [preposition + noun + preposition] structure, and they can create both adjectival and adverbial sentences (e.g. "A lawn in front of the house" (adj) vs "I played in front of the house" (adv)). "as regards" is different though. If you take "as" as a prep (which is odd in itself) and "regards" as a noun, then how does "regards" connect with the noun that follows it ("as regards [] the airline")? There is no magical way by which two independent nouns are "just" connected with nothing in between. I believe "as" in this case is a relative pronoun and "regards" a verb (the "s" indicates a third person singular case), similar to "which" in "a topic which touches on an array of subjects". If so, the most natural way to use it is after a noun (or a noun phrase or clause), as in "Speaking of your suggestion as regards the future direction ...", "his remark, as regards ...", etc. If you follow this thought, then using "as regards" in the beginning of a sentence is like using a relative pronoun without the antecedent noun. So some conservative people, like the person who corrected your writing, might find it improper. But it appears it has become commonplace to use it in the beginning too, as many dictionaries list such examples. So it's probably not worth much thought beyond a curiosity.

I do not think that there is any practical difference.

They are used to mean the same thing. I think in regard and regarding are more common. like: "kind regards" "best regards" or just "regards" is often used to finish off​ a letter to someone.