Spotted Mandarin and Psychadelic Mandarin?
 

Is it possible to keep both of these fish in a tank together? (one of each)

The tank would be 165G with probably like 200 lbs of live rock and at least 6 months established.

as long as you have one male and one female I doubt they care what color the other is. 2 males will fight.

Ok, so I dont really understand what the difference is in the species, would they mate if they are not the same species? Are they basically the same in terms of needs?

I have 2 psychadelic and 3 spotted in my 300gal and they all get along fine, all five hang out and feed together, I have not witnessed any aggression and all are fat and healthy, I suspect my success is partly due to the amount of space they have so if they decide they need personal space it is there for them.

I think your tank is a little young. Wait for late fall.
I would recommend a pair as well.
You can order a pair or take your chances.
Your odds are best if there is a large selection because you will want to buy the largest one which is male and the smallest one which is likely female.

I made a boo boo not too long ago trying to get a female for my male psychedelic. Watched the little bugger for quite a while at the LFS and was sure it was a female, but when I put it in my tank and it finally fully extended it's dorsal fin, no doubt that it's another male. Anyhow, so far so good and there has been no conflict between the two. There's a significant size difference between the two and I've witnessed the larger (original) dude make the odd move against the tiny newb, but nothing serious and definitely no damage. Generally they keep out of each other's hair and do what mandarins do all day, browse, eat, browse, eat... All this may change once the newb gains more size, time will tell and I'll be watching closely. Actually, the large male is having quite a time battling his reflection in the tank bottom where my Maroon Clown female keeps digging a hole right down to the glass. I've never seen him show anything near like that kind of aggression towards the small male in the tank.

Still would like to get a female but definitely won't do that until I catch one of the males and trade or sell it. They may be slow and methodical, but trying to catch one with all the LR is pretty futile. At some point I'll be setting up a larger tank and that will likely be the time I corral one of the males and trade him in.

As for the difference between the spotted and psychedelic, I think other than the coloration, there really isn't much. Feeding and care would be identical, no idea whether they would get along in the same tank, many variables at play here. Since starting this hobby I've gotten the impression that often fish of the same species have different personalities, what works for one person may not for the other, it's a bit of a crap shoot sometimes.