The two are almost completely synonymous, with the only difference really being that alright is more informal.
From Merriam-Webster's definition of alright:
: all right
In other words, it means the same thing.
Merriam-Webster's entry also adds the following:
all right or alright?: Usage Guide
Although the spelling alright is nearly as old as all right, some critics have insisted alright is all wrong. Nevertheless it has its defenders and its users, who perhaps have been influenced by analogy with altogether and already. It is less frequent than all right but remains common especially in informal writing. It is quite common in fictional dialogue and is sometimes found in more formal writing. // the first two years of medical school were alright // — Gertrude Stein
In addition to all right being more relatively common (although alright is not uncommon in its own right) and formal, there might also be another stylistic reason to use it. As in the explanatory paragraph above, if you are comparing two opposite things, there would simply be a greater sense of visual parallelism to describe them as all right and all wrong as opposed alright and all wrong.
Other people might have different personal reasons to use one over the other.
But all of that aside, the actual meaning of the two words is effectively identical.