Generally you buy them separately, unless it was a “pelham bridle” that came with two reins (do not see many of those sold any more).
Generally, “bradoon reins” (ones designed for the bradoon bit on a double bridle) are thinner than a regular rein. Often a bradoon rein will be matched with a regular set of reins (rider’s preference, laced, rubber etc).
Personally, I used to ride with two reins (for my gag bit), and I used regular laced rein for the main snaffle rein, and a thinner plain raised (raised, but no lacing) bradoon rein on the gag part.
Comes down to rider preference, and the reins are usually mixed and matched.
I bought mine separately when I used a bit that needed two reins. I bought a thinner, flat curb rein for the leverage part of the bit and then had the laced reins that came with the bridle for the snaffle. I did use another bridle that just had two regular reins and actually preferred that feel. I haven't ever seen bridles come with two sets, all I've seen have been mix/match.
When I rode with a pelham or a gag on my old jumper I used rubber reins for the snaffle rein and thin plain curb reins for the gag/curb part. I know someone who used two sets of rubber reins but that was way too much stuff in my hands, even with the thin, flexible rubber ones.
You can take a line and say it isn't straight- but that won't change its shape. Jets to Brazil
When I'm organized and planning on riding with two reins I use a regular laced rein on the snaffle ring of my gag and a flat/unlaced curb rein on the gag ring.
When I'm disorganized or throwing together a bridle at the last minute I often end up using two sets of laced reins.
I don't notice much of a difference between the two setups, but in theory I much prefer the smaller curb rein as that second rein. I don't think I could handle two sets of rubber reins.....holy blisters, Batman!
I use rubber reins on the snaffle and for the second rein I use web reins with stops, rubber lined reins, or laced reins. Plain reins get slipppery when a horses neck gets sweaty. Depends on what you like though. I have long fingers and big hands so they fit easy in my hands, but with smaller hands you have to consider width and such.
I am on my phone 90% of the time. Please ignore typos, misplaced lower case letters, and the random word butchered by autocowreck.
I don't have very big hands, but I prefer thick reins. So I use a thick rubber rein for the snaffle, and then whatever else I have around for the curb. My preference is a set of plain leather with rubber lining the inside. I've also used rubberized web reins, laced reins, and plain curb reins. I find that it's really hard to hold thin curb reins with thick rubber reins, so I only use plain leather curb reins if I my snaffle rein is also thin (ie laced reins)
On my hunter/eq pelham I use a pair of laced reins and a plain thin curb rein. On the jumper one, I use rubber reins or rubber lined laced reins (though sometimes I use those on my eq bridle, depending on if I think it might rain) and brown rubber lined curb reins that I found on consignment ages ago, however I've never seen them recently.