hey timeking.. first, welcome to Automotive Forums..
now, hopefully, at least one (of hopefully many) answers on your tech question..
first, you are right; the tire manufacturer is required to meet, or exceed, certain specs upon designing their tires, and have charts.. but they are quite well hidden..
classictrucks.com in the late 90s did a complete article and rundown on how to read the side of every tire on the planet.. it is in their archive DIY sections; and if you cannot find, i have a copy that i can post, or email..
that said, onto portions of your question.. you mention RAM1500, the Dodge became the RAM1500 back in '94/96.. i do not know which year/model you have, but from the late 90s to the newest '21 RAM; tires (in make/model/size) have changed in design..
in the mid/late 90s, your rig was running 225/75/15s to 245/70/16s; and the brand new '21 base (Tradesman) can run from a 17-18", and the more elite models can have up to a 22" wheel/tire combo..
that said, depending upon diameter size, aspect ratio, tire hardness, and load index (and sidewall) can justify different psi ratings..
so, if your truck has on its placard says load index 115, that is about 2400lbs. that your single tire can carry safely; regardless of psi..
psi should be as close to max as possible to insure best overall mpg, and to assist the speed factor, which allows a tire to travel at 'X' speed w/o allowance for that 'squishy/spongy' rollout as you round a corner and inertia and weight bear down on the tire's sidewall, as the geometry of forced mass changed the amount vehicle weight shifts from center mass of tire attached to earth, and moves to outer rim areas..
so---
Q1- if both 44 & 51 psi tires are rated at 115 then amount of load/weight they can carry are same.. a 51 psi tire will get poorer mpg at 40psi than a 44psi tire..
a 51 psi tire will be able to handle more mass at speed than 44, as weight has to do with stationary downward gravity, mass is inertial property or 'matter' and directional movement..
Q2- yes, rolling resistance of 51psi on your rig with moving mass in bed and on tongue will be the best overall for mpg and to assist in removing "roll" or spongy cornering..
the 51 probably has a higher treadwear number, as a 250 would perform two and a half times better than a tire with a 100 rating.. and it might have a better traction or a better A/B/C grade, as its ability to absorb and dissipate heat will be better..
if you want more info: coker tires has a more complete physics course than i can type..
coker.com or 800-251-6336
sorry for being wordy... but i hope this helps..