Gravlax, lox, and smoked salmon are all types of cured salmon. How exactly they are cured is a bit different, making one of them extremely easy to make at home and the others a bit trickier.
Gravlax is cured salmon. It is a Scandinavian specialty that is remarkably easy - and well worth the little effort it does require - to make at home. To make gravlax, you simply cover salmon filets in a salt-sugar mixture (most people, yours truly included, use a bit of aquavit or vodka and some pepper or herbs to the mix) and press them with weights as they chill to remove water from the fish and infuse it with flavor. The result is a firm yet silky texture and a salmon that tastes a ton like... salmon. Gravlax is traditionally served sliced thinly on rye crackers or rye bread with cream cheese, and maybe some slivered red onion.
In case it isn't obvious, I'm a big fan of gravlax. It wouldn't be Christmas Eve at my house without it - I once even cured two salmon filets in a cooler in the trunk of the car while we drove for two days to our destination for the holidays. While I usually save it for the Christmas season, it's an impressive crowd pleasing dish for parties of all kinds. See How to Make Gravlax here.
Lox is also salted and cured (allow to sit covered in salt) much like gravlax. Lox, however, is then briefly cold-smoked - usually. Sometimes lox is just cured, like gravlax, although with a cure that is heavier on salt and without pepper, alcohol, or herbs added in. Lox is usually served in long, thin slices with bagels and cream cheese, often with slices of red onion and tomatoes and perhaps a few capers for people to add, if they like.
Smoked salmon is a term usually used to describe salmon that has been hot smoked. These salmon filets are usually covered with a spice rub that may have sugar or pepper in with the salt, and hung in a smokehouse where the heat from the constant smoke slowly and gently cooks the filets while also infusing them with tons of smokey flavor. Luckily, a full smokehouse isn't absolutely necessary. You can smoke salmon on a grill (see Smoked Salmon On the Grill) or even on a stove (see How to Smoke Salmon Indoors).