I was wondering the same thing. But some of the backstory I've been reading about the Resistance leads you to believe that they're a smaller force that's working outside of the parameters of the New Republic. And perhaps they're not as well equipped as the Rebel Alliance around the time of the Battle of Endor. I do recall some dialogue from the movie that said the attack from Starkiller Base on Hosnian Prime likely destroyed the Republic Fleet.
I did a little reading on Wookiepedia and here's what's out there:
-The Galactic Civil war went on for a year after the battle of Endor. The Empire had a deveastating defeat at the battle of Jakku...and they signed a peace accord with the New Republic.
-After the battle of Jakku, many Imperial Commanders took their ships and fled to the Unknown Regions...they later returned as the First Order and started building up their military in violation of the Peace Accord.
-The New Republic, seeing the mistakes of the Old Republic and wanting to get away from the shadow of the Empire, moved the Capital of the New Republic from Coruscant to the Mid-Rim Hosnian system. They also effectively demilitarized by dismantling many of the ships in their fleet. They still have the largest fleet in the galaxy, but it is nothing like the size the Alliance had in the Galactic Civil War.
-Princess Leia, seeing the intelligence reports that the First Order is in violation of the Peace Accords, leaves the New Republic Senate and starts the Resistance. She recruits many military commanders who were out of a job with the New Republic demilitarization and has spent nearly all of her political capital in doing so. Although the Resistance is not formally recognized by the New Republic, they do offer under the table assistance and the Resistance has the support of many of the Senators.
Hope this helps.