I never ever thought I’d resort to this as a parent, but…
Bribery.
When the Skeezling was a month or so past her second birthday, we decided to try and persue potty-training a bit more aggressively. She’d used the potty seat a few times successfully, but wasn’t interested enough to want to use it every time. We figured we’d try a little bribery, for a month, and see how it went. One M&M for pee, two for poop.
In the span of a week or so, the kid dirtied exactly two diapers, and we ended up giving away most of the last package of diapers we’d bought.
There was another incentive, which worked wonders for us. Panties. She’s crazy about the Hundred Acre Wood gang (Tigger, Pooh, and that bunch) so we found some Pooh-Bear panties, and talked 'em up in a big way. Big girl undies, with the sacred bear all over them, which she could only wear if she could use the potty-seat regularly.
A week. I was floored. We had prepared ourselves for a month of candy (and the subsequent hyperactivity) and having to go back to diapers for a while before trying again.
And if, like me, you’re not all that comfortable with the sugar bribery, after three days or so, start “forgetting” the M&Ms as often as you can get away with it. If the kid doesn’t mention them, you’ve scored. She used the potty-seat, on her own initiative, and without candy. Win-win. After the second week, there was no mention of them at all.
By the same token, we also had the problem you describe genie, with one form of elimination being more acceptable to the kid than the other. She got over it fairly quickly, but some kids don’t. Patience is, as always, your best weapon here.
A Digression:
If, right now, you think I’m full of shit (no pun, really) or you believe me, but hate me anyway, it’s cool. Our pediatrician suggested to us at the kid’s two-year-old checkup visit this idea, and bragged to us about how she had potty-trained her son in about a week. We were convinced she had to be pulling our legs, or had some secret pediatrician’s knowledge of potty-training that mere civilians would never understand. But it works (for some kids, at least.)
Good luck, in any case.