No it does not end at 2 years old.
It can go on and on... even until adult hood, IF a child is not guided or taught on how to express themselves and communicate and how to "cope" with emotions and how they feel and during stresses or disappointments.
But yes, at this age, they can be moody and fussy.
At 3 years old too.
And so forth.
Just teach him the "names" for feelings ie: mad,sad,happy,frustrated,irritated,hungry,tired, angry, etc. That way, he can pinpoint how he is feeling and to articulate it....then tell you. That it is okay to tell you how he feels.
Then just teach him "how" to cope. If he is mad, its okay... but if he is hitting then redirect him to something better. Encouraging. Or to hit a pillow. That hitting people is not allowed etc.
They are just learning at this age. They will make mistakes. They will test limits. They will seek independence and protest at times. All developmental based and normal. But give him the "tools" to manage.... age appropriately. Meaning, don't expect him to react/handle something like how a 5 year old would. There is also the 'maturity' of the child too... so just guide him.
Usually a kid gets mad because they are frustrated. Or, they want to do something they have in their heads, but can't actually do yet. Or, they are told "no", or they want attention or need something even comforting.
I have found a good way to deflate an angry child, is to hug them, and then try and make them laugh! Distracting them.
All the best,