At a basic level, a road bike has drop bars and integrated brake/gear shifters (Shimano is branded as STI), a tri bike has triathlon specific handlebars (tri bars are where you rest your elbows on pads and have your arms reach forward over the front wheel) with the gear shifters on the ends of the tri bars.

It really depends on the type of rising you are planning to do. While I haven't raced a tri in 10 years, I still have both a road bike and a tri bike, each has a specific purpose. If you only want one bike you need to work out what you want it for.

You have a few key decisions to consider up front.

First is dedicated tri bike versus a road bike. A tri bike is faster and more comfortable in a race. But they are specialized and kinda suck to ride anywhere else. A road bike is more versatile, and IMHO far more fun and comfortable to ride outdoors in training and group rides. So, if you think you might want to ride outside and with others, consider a road bike. If you want dedicated performance, then lean toward a triathlon bike.

It sounds like you are familiar with bikes in general. So, you probably know that the "brand" of a bike is merely the frame. The components are the same across all brands and either Shimano or SRAM, and within those, either mechanical or electronic.

I could list a dozen mainstream brands of bikes (Trek, Specialized, Giant, Felt, Canyon, Cervelo, Cannondale, Ventum, GT, Orbea, Ribble, Ridley, etc.) and still leave many out. These are all good bikes that will perform well and hold up. Most of them have a full spectrum of options from entry level to bikes they put in the Tour de France. So, it often distills down to a cost decision and condition of the frame and components.

I would not get components less than Shimano 105 or SRAM Rival. These are their entry level sets for regular road riding. Also, I prefer both of their 11 speed offerings, because they have better cassette choices. So, if you are shopping used, no worries about 11 speed versus 12 speed. 11 speed is great.

And if shopping used, I would not worry about rim brake versus disc brake. Shop overall value first, and you will be fine with whatever brake types the bike has.

I'd say you both could find reasonable road bikes to start your triathlons, and you can find some good used ones for $500-$1,000. You don't need anything fancy. I started five years ago on an aluminum Trek I found for $400. I think it was a 2007 model. It was fine for starting out. I bet if you go to your local bicycle shop and tell them you just want to start riding with road bikes, they could point you to good used ones. They won't necessarily have any, but they'll either know someone or will tell you whether FB marketplace, Craigslist or some other platform is the best place to look.

You'll also want to ask them to recommend a size for both of you.

Then when you get them, take them to the same shop and have them do a full tune up. If the bikes are in reasonable shape, it'll cost $150 to $200 and you'll know you're on a safe bike. They might even help you set up the bike so they fit you (saddle height is very important).

You'll see a lot of different bike at races. Some will be the top of the line and obviously faster than your bike. Others will be road bikes like yours. You'll see vintage bikes and flat-bar bikes.

I think you just want something to start riding, that doesn't cost a lot. Then after several months or a couple of years, you can decide if you want to upgrade. I first upgrading the mechanics on the old Trek and then replaced it with another used bike after about a year. That other used bike was also a road bike and it's still my primary bike.

Good luck.

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Not a coach. Not a FOP Tri/swimmer/biker/runner. Barely a MOP AGer.
But I'm learning and making progress.

Where do you live?

Plenty of people use a mountain or hybrid bike for their first few triathlons. Unless you think you are racing to win your first tri, no harm in using your current bikes if the ride is 25 miles or less. Plenty of other things to figure out before you worry about getting a new bike.

If you find that you do like triathlons and want to race more than once a year, then get a road bike. Any major brand is fine. I would shoot for trying to find a 5-10 year old bike for around $500. The downside of buying used is that you could spend way too much on a crappy bike or buy something that doesn't fit because it is what is available.

After riding around on a road bike for a while, then you can think about adding clip on aero bars.

After a season on the road bike if you are still excited about tri life then start shopping for a tri bike.

Ignore all this advice if you have already signed up for an Ironman and want to be competitive in your first race.