Several House Republicans have begun to float what they characterize as a "middle-ground" position. Instead of providing unauthorized immigrants with a path to citizenship, these Republicans suggest a path to permanent residency. Democrats have fairly strongly staked out their position: a path to citizenship (a difficult path, but a path nonetheless).
Under the structure of either proposal, unauthorized immigrants will be afforded a benefit that permits them to remain in the United States. But there are some important distinctions between a green card and citizenship papers. If you are a citizen, then you cannot get deported (unless you engage in actions that lead the government to try to strip you of your citizenship, which is incredibly rare, and the government is successful, which is even rarer).
However, even with a green card, certain actions may still render an individual deportable. For example, a conviction for certain crimes will permit the government to initiate deportation proceedings (technically called "removal" proceedings). Some of the crimes that could render a green card holder deportable are fairly reasonable, but others are much more contentious. The most contentious crimes concern controlled substances, and some advocates believe that the list of controlled substance crimes that can lead to deportation proceedings is way too expansive. Many are surprised to learn that the government has argued that for purposes of immigration law, possessing a small amount of pot on two occasions would qualify as an "aggravated felony."
Being a citizen also means that an individual doesn't have to feel as if they are an outsider or feel apprehensive that the government officials and institutions they interact with might subject them to heavier questioning, harassment, etc.
So either way, an unauthorized immigrant would have the benefit of being able to stay in the United States, but there certainly are distinctions. It will be interesting to see how Democrats value the path to citizenship as the debate roles on in the next few months. Will they cave on their request for a general citizenship path to obtain certain concessions from Republicans or will they hold strong to their position? Or, will there be a quasi-concession, where Democrats insist on a path to citizenship for younger unauthorized immigrants who came to the United States as children, but relinquish on the path for older unauthorized immigrants?