I'll start with I've got 34 years experience as a full time locksmith (1986 to present).
The first lock is what is known as a mortise lock. Back in the 1960s and before, there were numerous manufacturers of that type of lock, almost all are now defunct companies, or no longer make mortise locks. Those with original key cylinders usually have the company name on the cylinder face... this one is a replacement cylinder (more on that below).
Mortise locks are still made, but can be very expensive, and sometimes difficult to match a replacement to. They can be latchbolt only, deadbolt only, or like this one, latchbolt and deadbolt in one unit. Not all specifications (placement of holes in the door, dimensions of lock body, etc) were uniform. Some were unique. I cannot determine who made that lockbody, even though there appears to be a shamrock logo in the end of the deadbolt. I'm not familiar with that company... as I said there were many, some only sold regionally.
Now for the good news. Almost all mortise locks use a key cylinder appropriately named a "mortise cylinder". And those are readily available today, in numerous key ways, and they come in different lengths. Mortise cylinders are threaded, a very fine RH thread, and screw directly into the lock body. This is a universal size, I've never encountered a mortise lock with a different thread pitch or diameter. They must be in the proper position to work properly, normally that is bottom of keyhole at 6 o'clock (if for some strange reason the lock got mounted upside down, it would be at 12 o'clock). Once threaded in deep enough for cam to turn and mesh with mechanism, but not TOO deep, they are held in position by a set screw that's accessible on the edge of the door's side of the lock body. It will be directly inline with the center of the cylinder. Most set screw heads are hidden under a trim face plate. They also use what's called a cam on the back of the cylinder. These are held on with 2 screws. Cams operate the inside mechanisms of the lock body and turn with the rotation of the key. Cam shapes can be unique and different for different manufacturers, and mortise cylinder length depends on door thickness. When replacing a cylinder, if the cam is unique, it can be removed from the old cylinder, installed on the new one. NEVER remove the cam screws with the proper key inserted into the cylinder, unless you intend to disassemble the cylinder for rekeying. It will come apart easily with no cam on the back and the tumblers "unlocked" by the proper key.
A standard entry door is 1-3/4" thick, and would most likely use a mortise cylinder length of 1-1/8", depending on trim plate thickness. They come in 1", 1-1/8", 1-1/4", 1-1/2". The mortise cylinder in this photo is not the original, it is a fairly recent replacement, and it appears to be a Weiser key way, but possibly a Kwikset... I'll explain why it could be either. Weiser & Kwikset have a keyway identical in shape, but as Weiser keys were thicker than Kwikset, the keyhole will be a bit wider on a Weiser. A Kwikset key most assuredly will fit. If it's wide enough to accept a Weiser key, then it's a Weiser keyway, if not, it's a Kwikset. Weiser keys will not fit a Kwikset, as they are just a tiny bit too thick.
Weiser & Kwikset locks can both be keyed to use Kwikset keys, provided a "universal tumbler kit" is used on the Weiser cylinders, and not factory Weiser or Kwikset tumblers. Weiser has 10 tumbler size lengths, Kwikset only 6. I use Kwikset keys for both, Kwikset tumblers in Kwikset locks, universal tumblers in Weiser locks size matched to Kwikset tumbler sizes.
Second lock in picture is a Kwikset copycat, a low cost, low quality, Chinese made knockoff of one, typically sold in home improvement stores. Genuine Kwikset deadbolts have the name Kwikset embossed in bolt's face plate on the edge of the door (older ones say Kwikset right on the faceplate of the lock). Knockoffs are blank faced like this one. These can be rekeyed using Kwikset keys and factory tumblers, as key cylinder dimensions are usually identical.
Rather than rekey these knockoff deadbolts, I'd recommended replacing with genuine Kwiksets. The collar around the key cylider is not "armored", it's just thin sheet metal. Kwiksets have a much better collar, and the cost between rekeying and replacing isn't that much more anyway. This is a double cylinder, key cylinder on both sides, and you would be charged for TWO locks when it's being rekeyed, because there are two sets of tumblers to be replaced instead of just one.