What are the differences between The State Versus Beaver Mar 26, 1958 vs Beaver Takes a Drive Nov 18, 1961?
Beaver’s age
The one who gets the tickets
Who goes to traffic court
The punishment given by the Judge
Any other differences in the two shows?

Well let's see. Just off the top of my head ( from my memory of seeing both episodes several times ) I'll bite.

Beaver's age

8 in the former, 10 or 11 in the latter. The timeline of both boy's ages varies in the show.

The one who gets the tickets

Beaver gets cited by the motorcycle policeman in the former, and it's Wally gets cited in the latter.

Who goes to traffic court

In the former, Beaver...and Ward...face the judge. It's Wally, and IIRC, Ward as well in 'Beaver Takes a Drive'.

The punishment given by the Judge

IIRC, no legal penalties as such in both episodes, but the judges mete out stern lectures in both cases, to both Beaver/Wally, and to Ward ( being responsible for his son's behavior ). I guess you can consider the warnings as a penalty of sorts, especially in Wally's case since he'll soon be seeking his drivers license and an official warning gives him that much less slack for wrongdoing, going forward.

Any other differences in the two shows?

Without more specificity in the question, I offer this/these:

In 'Beaver Takes a Drive', while Ward is upset, he doesn't directly punish Wally/Beaver, but in 'The State vs Beaver' Ward confiscates the Go-Cart for Beaver disobeying his order not to drive it without Ward present, just as Ward threatened he would.

In the former episode, Beaver completely folded to Larry's pressure to drive the Go-Cart, whereas in the latter episode, Gilbert, manipulative louse he usually is, doesn't try to dare Beaver into actually driving his father's car, but just to pretend. Releasing the parking brake and coasting into the street was all Beaver.

Releasing the parking brake and coasting into the street was all Beaver.

And, predictably, Gilbert, weasel that he is, immediately ran away.