You can tell he's older now because they gave him a beard.
This raises a lot of questions, chief of which is how Richard could have possibly survived the plane crash in the flashback that kicks off the movie. He kind of glazes over that and mumbles about how he needed to disappear to keep Peter safe from the villainous Oscorp. Peter gets angry at his father, then hugs him, which makes us wonder if this scene was cut because too many fathers and sons who went to the movies for some light male bonding would have been forced to uncomfortably examine their own relationships.
"You think Peter's dad is proud of him? Then why did he never get him the Tonka Truck he wanted?"
Richard then reveals the reason he came back -- he promised Peter's mother that, if the time ever came when Peter needed him more than anyone else, he would be there for him. Aw, well that's a touching example of fatherly love that ... wait a second, what?
Now's the time that Peter needs him? Not when Richard's own experiments were putting Peter's body through insane modifications? Not when Peter was fighting a scientist from Oscorp who turned into an evil, superpowered lizard-beast (also thanks to Richard's research)? Not when he battled another Oscorp employee turned evil by electric eels, or the son of the CEO who armed himself to the teeth with futuristic weapons? Dude, if your disappearance was intended to protect Peter from Oscorp, then you did a pretty shitty job.
"AND THEN THAT GUY STARTED ATTACKING ME WITH BOLTS OF DUBSTEP!"
It comes across less as an amazing revelation and more as another forced plot twist in a movie that's already jam-packed with them. But at least Richard was able to deliver a certain famous line that they were apparently too afraid to use in the first movie.
"With the great idea to abandon your son comes a great deal of money saved on college tuition."