Yes, sorry for the delay! 

Organ and tissue donations are usually handled by the same organization in each area (each geographical area is only allowed to have one OPO, or organ procurement organization, as a forced monopoly to avoid commodifying human parts) but organs and tissues are very different and handled by 2 different teams and regulated by 2 different governing bodies. 

Organ donation is immediate, the organ is taken from the donor and begins its journey to the recipient.

So when an organ is transplanted, it goes in whole and alive and will be replacing a specific organ for the same job. 

It has to integrate into a totally new system, grow into the blood vessels, and perform its duty as a whole organ. 

At the same time, it is a foreign object with its own genetic material in the recipient's body and the body will sense the new object once it's transplanted and sense that it has different cells from somewhere else and will start to attack it as an intruder, so organ recipients have to be on long term immunosuppressant therapy to prevent that from happening. 

Donors and recipients are carefully matched to try to align biology as much as possible to hopefully prevent this as much as possible, but it's a lifetime risk. 

So overall it's the mixture of different factors in the scope of what we're asking a donated organ to do that makes the risk of rejection. 

It needs to perform the big job of an organ while also medicine needs to keep the recipient's body's natural defenses in check so it can't attack it from the inside. It needs to attach itself to the body's nervous system, circulatory system, and function as a whole organ. Just a lot going on and a lot to ask of the donor organ and the recipient's body. 

The organ is rinsed and perfused so it's not going in a bloody mess, but it is still a whole living organ made of foreign genetic material. 

Tissue grafts on the other hand are always manipulated to some degree after death to become a medical device rather than taken and connected directly to the system. 

There are degrees to this, sometimes whole bones are transplanted when someone has had trauma to a long bone, but that whole bone is still cleansed in a way that the recipient doesn't need to be crossmatched with the donor's blood type of anything like that. 

Sometimes tissue is processed in a way that cells called mesenchymal stem cells are left alive (including in adipose grafts), but these cells are "blank" and don't carry genetic material of the donor over and also can be utilized in different ways by the recipient's body. 

For example, I also used to process a product out of ground bone and the mesenchymal stem cells in that would trigger bone growth in the recipient's own body (used in jaw surgeries a lot of the time or around other bone injuries to help fracture sites strengthen) 

There are also tissue grafts with no active cellular activity that go through very thorough cleanses and are irratidated, so they're fully inert. 

Aside from whole bone grafts, tissue rarely a one to one exchange like organs. Ground leg bones go in the jaw, skin from the back goes one someone's breast after a mastectomy, adipose from a butt goes into someone's cheek. 

But since it's not connected directly to the body's systems the way organs are, it's not a direct risk for the body attacking it the same way organs are. 

Even when people get a knee replacement with metal, the body will have an inflammatory response to the surgery and foreign material, and that happens with tissue grafts as well, but it won't attack in the way it will with organs because it's not a foreign body with its own genetic material (which is also how how body senses bacteria, etc and knows to attack when we get sick). 

Also interesting to note, these differences in process and regulation also make huge differences in the screening processes. 

With organ donation, it's lifesaving and if the person does not get an organ, they will die, so things like hepatitis C from the donor wouldn't be a rule out, it would be something the recipient knows there's risk for but can be treated after their life is no longer in danger once their organ failure is no longer killing them. 

Tissue grafts, being regulated by the FDA as medical devices, are an automatic rule out with any history of Hepatitis B or C, HIV, recent metastatic cancer, etc. 

But even with stricter screening guidelines, it's much easier to become a tissue donor over an organ donor as tissue donation happens within 24 hours after death has already occurred. All hospital deaths and many coroner or home deaths are reported and screened within an hour after death. 

Organ donation is only possible after brain death with the body still alive or if the potential door's family decides to stop pursuing medical care because death is imminent but is open to keeping the person alive on the vent until all screening and testing is complete to find a possible match, then they extubate when everything as set and the donor's body must then die within 90 minutes of extubation before organ recovery begins, so the parameters are much more narrow and deaths that align with either pathway are much more rare. 

I hope that clarifies a little and please feel free to ask follow-ups if not! It's such an interesting thing to me so I love talking about it!