Originally Posted by X Mode
The former acts as a conjunction, whereas the latter a preposition. :D
But I don't think it's alright to change your original sentence into a present participle one. Like, "Having dinner, I stepped outside for some fresh air." This gives me an image that the action of 'having dinner' and 'stepped out' happened concurrently. If I rewrite the sentence to "After I had eaten dinner, I stepped out for sme fresh air," however, it sounds perfect to make it a present participle form as in "Having eaten dinner, I stepped out for some fresh air."