Since the objects have the same Dec, you just subtract the RA's of the two objects. So I'm kinda lost as to what the user was asking for.

Doesn't work like that.

To belabour it.

For a sphere's surface you don't have lines you have arcs, the arcs that go all the way around and meet themselves are called Great Circles. When you see a full map of the sky with RA and Dec grids this is showing those.

Now, declination, just up and down, the lines never join. 10 degrees is ten degrees from 20 degrees, as is 30 degrees to 20 and 90 to 80. This is true no matter what RA you are at.

Not true for RA. The gridlines of RA meet at the poles (singularities, the word has a more general mathematical meaning than what people usually associte it with, pretty much for our purposes thing a 'POINT' in some geometry or other), and as we are talking arcs the distance between RA 1 hour and RA 2 hour is a different number of degrees at 10 degrees declination and 50 degrees declination and differenter again at 80 degrees declination.

Back to measuring RA and Dec.

Dec is in degrees, so we've got that sorted, distance apart in degrees is just big number minus smaller number.

RA is in hours, going back to the traditions of how it was measured (it used to be the most precisely measurable if you go back long enough, and in fact measuring declination was tougher and often "polar distance" was measured instead, that is the distance from the Celestial Pole). Clocks and passage of time were used. Remember, a time zone will have been applied, or a different prime meridian (people didn't always use Greenwhich, the French used one based at Paris Observatory for a long while). That gives you a zero point. Then you can add up that such and such a star transits four hours later than noon on a set date (Vernal Equinox my memory says) so the RA is 4 hours... Something like that, don't take my exact word for it. You know where your Central Meridian is, that's the point due South (for Northerners), and from that you get your Transit time, the time it passes the Central Meridian, that is stops being to the observer's East and starts being in the observer's West, or if you like it is no longer rising and is now setting. Time difference that from the time of your reference point and you get your RA. My wording may be a bit problematic here, but that's the sort of thing though I may have forgotten a nuance or three.

That gives us 24 horus or RA. There are 24 hours of RA to a Great Circle at the Celestial Equator (remember, the Earth is tilted according to the Solar System orbital plane)

Sometimes you want to make your geometric adding up and subtracting and jiggling in general easier, so it is better to have both RA and Dec in the same units. Either degrees or sometimes radians (as long as you consistently use one or the other, we'll stick to degrees).

360 degrees to a circle, 24 hours to the Great Circle. Degrees to hours of RA is 360 / 15 and hours of RA to degrees is 24 x 15.

But look at a globe, the Great Circles get smaller as they approach the Poles. So simply going 24 x 15 for all declinations is going to be WRONG.

It turns out that the trigonometry juggling you have to do ends up meaning you need the cosine, the adjacent line of a right angled triangle divided by its hypotenuse, which as has been said earlier meant cosine tables when I was at school, now you mouse click on a button on your computer's calculator or you go =cos(x) in your spreadsheet. No more printed trig tables or log tables until the great EMP disaster of 2037.

Nearly there, hold on!

After all this wittering and juggling we come to this

Degrees of declination are in degrees.

Degrees of RA are = RA in decimal hours multiplied by 15, to get assumed degrees. Then because the Great Circles differ in size dependant upon their Declination, we have to make a correction, so the value in these assumed degrees just so happens to need to be multiplied by the cosine of the Declination in degrees.

Or in short

RAdegrees = (RAhours x 15) x cosine(Declinationdegrees).

Which is simple enough but a bit of a bore in practice especially if you are doing lots of them at a time by hand with pen and paper or calculator.

For example, I sometimes have photometry datasets I've found that I want to match on position with other datasets, but the first is older so the RA and Dec so the RA and Dec are in sexagesimal (RA HMS.s Dec +/-D'"), converting Dec is easy enough (degrees + ' / 60 + " / 3600), and you can do that for RA too except using hours * 15 for 'degrees', BUT you also need to do the multiplication of RAdegrees by the cosine of the Declination in degrees. Basic stuff but mentioned in pedantic bits very longwinded.

Simple key presses on the calculator but the datesets have tens of thousands of positions and you need both in decimal degrees in order to cross match them on those positions.

So you use the formula in a spreadsheet and copy it down for all the rows of the dataset in question, then you can match positions on decimal degrees.

Or someone does an excel sheet that takes an sexagesimal RA and Dec at a time and coughs up the answers in decimal degrees.

Actually, in the past few years I just use something called CDS XMatch, an online browser front end to a CDS service, and as that sometimes starts choking when crossing big datasets I increasingly use TopCat which has a CDS XMatch.

There, far, far, more than you ever wanted to know about why RA2 - RA1 does NOT equal the difference in degrees. Some of it may even be correct.