Actually starting 2 companies at the same time? Yes, that is crazy. In fact, you're arguably crazy to try to start 1!
However, when we started we had 2 - not really overlapping though. Had two separate sets of business cards. And we may have even thought we were going to start both (I don't remember what we thought).
What ended up happening, however, is one gained traction faster than we expected and the other got stuck really fast. In other words, it turned out we were just vetting ideas - but maybe taking it (and ourselves) a little more seriously than we should have. Or maybe as exactly seriously as we needed to - we were all in, mentally.
It wasn't a bad thing - yes, others thought we were crazy and acted like we were, but it kept us thinking laterally at the beginning. Once investors were involved though, we made it clear it was the same company (not a side project) and they were investing in us and all of our time. Further, by that time, it was clear we were pursuing the one with the faster traction full-time (not because we "killed" the other one, but just because it was the one we wanted to work on).
So, I'd say don't be afraid of this, but equally maybe don't think you're going to have two independent legal entities you split your time on and have different investors on in a year. Equally do not think it somehow gets *easier* past the initial stages. We thought we were working "so hard" initially. Now in retrospect, we kind of laugh at ourselves - those were the easy days! We had time to think about things like 2 different startups!
I can't quite tell from your post if this is your situation, but the thing to be deathly afraid of is not two different startups (it will figure itself out - you don't need anyone's advice), but two different business plans for basically the identical market.
In this scenario, you are dividing your efforts and there's unlikely to be a natural culling here - most likely both approaches will fail and you'll conclude the market just isn't ready for you, when in fact that may not be the case. You have to make a call on a business plan - change it all you want, and successively try new paths, but 1 market = 1 strategy or else you're not going to get anywhere (in my experience at least - we did a lot of strategy hedging early on and really only made traction when we were willing to suck it up and make 1 choice, risking being wrong, but putting everything we had towards the goal).
You can't get real feedback from customers when you show up with 2 totally different solutions/products. They get confused and start thinking you're a custom dev shop - and so they start asking for things they wouldn't have asked for if you had just kept it simple and shown them one. You can try to split your customer list, but now you're really dividing your opportunities; plus when the meeting is going poorly, you'll probably always pull out the other product.
With two different markets, you're not compromising on anything except your time - and early on, it can be a good thing to be thinking widely: it can keep you moving forward on something, rather than getting stuck and burning out on a startup that was never going to make it for a reason you didn't understand when you started and weren't willing to consider once you were into to it.
Anyway, hope this helps - good luck! Most of all, though, don't worry too much about being "wrong" here, whatever you decide to do. Stay open-minded and keep learning!