The Knicks know who they are, and they know who they want to be. They are a good team that is in a prosperous stretch — five wins in a row, seven out of eight, 17-9 since they were last at .500 three days before the New Year. They are a good team with ambitions of being very good.

The Celtics checked the boxes for “good” and “very good” a long time ago. They are a great team that fell two victories shy of adding an 18th championship banner last summer, and most nights they look like an awfully good choice to be riding in duck boats through the streets of Boston come late June.

The Celtics sit in first class; the Knicks are still in coach.

It’s what makes Monday night at Madison Square Garden so much fun. The Knicks will be taking a step up in class, a middleweight challenging a heavyweight. There is no belt on the line and little on the table; the Celtics are 10 games clear of the Knicks in the loss column. The Knicks’ neighborhood includes the Cavaliers to the north, the Nets next door, the Heat and Hawks and Raptors to the south.

Still, this is a chance. This is an opportunity. This is a night when the Knicks can provide a little more testimony that they can be more than just a nice little story come April, when the games start to matter a whole lot more.

“We’re playing well,” Knicks coach Tom Thibodeau said the other night, “but in this league you’d better not take a night off because teams will make you pay when you do.”

The Celtics will make you pay, even when they’re banged up. Boston announced on Sunday that they will be without Jaylen Brown at the Garden because of personal reasons. But the Celtics have proven all year that they can keep winning even when they’re down a starter or two, down a star or two.

And if the game doesn’t mean much in a tangible sense to the Celtics … it’s still the Garden. It’s still New York City. And the Celtics are still the alpha dog in the Eastern Conference that wouldn’t mind sending a message to a batch of feisty Knicks, feeling their oats:

Stay in your lane.

And not the passing lane.

“We expect a lot out of each other,” Celtics star Jayson Tatum said Saturday night in Philadelphia, after he hit a clutch game-winning 3 (and after Joel Embiid’s 70-foot heave splashed just after the final buzzer). “We trust each other, and we know every game everyone has to contribute.”

That Celtics-76ers game Saturday — a 110-107 Boston win — was a reminder of precisely what the caste system in the East looks like. The Bucks won again Sunday, their 14th straight, to stay a half-game behind the Celtics (44-17). The Sixers, at 39-20, join those two teams as the acknowledged top flight. And that isn’t likely to change.

But now the Knicks find themselves with an opportunity to be very much in the conversation for the next level. The Nets’ buzzer-beating loss in Atlanta Sunday drew the Knicks even with them for fifth in the East (even if the Nets’ still have a .002 edge in winning percentage). They are 2 ½ games back of Cleveland for the fourth seed.

Finishing fourth or fifth is a huge carrot to pursue because it allows you to avoid the Top Three in the first round. Again: For the Celtics, that is more a formality than a goal because they’ve won at least one playoff series five of the last six years. For the Knicks? That would be a gigantic leap forward.

So they inhabit different solar systems here. But in the same way generations of suburban jump shooters have dipped careful toes in the water at the West 4th Street or Rucker playgrounds in search of stronger competition, so will the Knicks engage the Celtics on what promises to be a snowy Monday night, in what ought to be a crowded building, playing as well as they have in years.

“I think it is really the chemistry outside of when we are playing basketball,” Immanuel Quickley said of the team’s present vibe. “On the plane, in practice, hotels, everywhere we are, we are really tied together, and it is leading onto the court. We have a lot of chemistry in this locker room.”

And have begun to generate a lot of buzz in town. Perfect time for a visit from the Celtics. Perfect time to see how the Knicks size up to the varsity.