My question is, will a 40R be the same length as a 38R, or is it a little longer?
Probably about the same length. If there's a difference - and there may not be - it'd likely be a sufficiently small difference that you needn't worry too much about it.
But speaking of length, what about sleeve length? If you're picking up the jacket today, to wear to a funeral the day after tomorrow, that doesn't leave much time for alterations. And while a need for some alterations can be ignored with a little effort, it'd really bug me to wear a jacket with sleeves a few inches too long. Oh well, I suppose you could just put up with it for the funeral, then have any necessary alterations done later on.
I've seen some of the charts saying something like anyone over 5'11" should be in an "L". But, my 38R seemed to be a perfect length. I'm 6'0".
There are retailers who suggest that men over 5'11" should wear a Long. And others who set the line at 6'1".
Ignore all this. Cuts vary. Men's builds - even for men of the same height - vary. Tastes vary. Only by trying on the jacket, will you be able to tell whether a Long looks better on you than does a Regular. If a chart says you should be wearing a Long, but the Regular simply looks better on you, you'd be a fool to obey the chart's instructions.
FWIW, I'm 6' tall. And I strongly dislike the current fashion for shorter jackets. And even so, many of my suits and sport coats are Regulars, not Longs.
So, a 50R is going to be the same length as a 40R, at least in the same model.
Maybe. But not necessarily. Even manufacturers who don't change the jacket's length with every size increment, may still opt to make their larger sizes - say, 48 and up - a little longer than their smaller sizes.
And at some point in the next few weeks, go get yourself a new suit. One that fits you now, not as you were a couple of years and 20 lbs. ago. Because a man should have at least one suit which fits him. Because you never know when you'll need a suit. For example, when attending a wedding or a funeral. (Particularly a funeral, since obviously they're more likely than weddings to happen on short notice.)
It doesn't have to be a particularly pricey suit. Even quite an inexpensive solid grey suit, which fits you well, is an enormous improvement over having no properly-fitting suit at all, and likely versatile enough to suffice for nearly any suit-worthy occasion in which you might find yourself.