FORT MYERS — The first time David Price climbed into a Red Sox uniform he said it felt a little, well, strange.

And then he went out and threw live batting practice.

Yesterday, with hundreds of Sox fans looking on from behind the fence at one of the practice fields behind JetBlue Park, Price threw his second live batting-practice session.

Did it still feel a little strange?

“That was a while ago,” said Price, after he’d aired it out against Blake Swihart and Rusney Castillo. “I think that was before camp started. But I feel good, I feel really good now.”

Yet we can all agree that Price’s first Fenway Park appearance — that is, at the real Fenway, not the lyric little toy box down here in Fort Myers — will be a bit of a culture shock for Red Sox fans. I’m not talking about the old dust-ups with David Ortiz, since that’s been put to rest, and I’m not talking about Price being “comfortable” in the clubhouse, the simple reason being that he happily bounces around like he owns the place.

David Price belongs with this team. Really. I’m not going to revise history and tell you guys like Carl Crawford and Adrian Gonzalez didn’t look like they belonged when they arrived for their first spring camping trip with the Red Sox, because that would be a lie, but again: Everything I see, everything we see, indicates Price will make it work. Spectacularly.

Still, I’m talking about the uniform. So many players come and go these days that in most cases the savvy fan doesn’t give it a second thought. Yet there are also cases in which we take a sort of snapshot of a player and post it on the wall inside our brains, where we expect it to remain forever.

The snapshot of David Price shows him in a Tampa Bay Rays uniform. He came up with the Rays in the last weeks of the 2008 season, raw but hugely touted, and just a few weeks later he blew away the Red Sox in three American League Championship Series relief outings.

Of his 104 career major-league victories, 82 of them were registered while he was wearing a Rays uniform. And while Price had stops with the Tigers and Blue Jays before signing with Boston, he never faced the Red Sox wearing the uniform of those teams. He has 11 wins against the Red Sox. All with the Rays. He’s 6-1 with a 1.95 ERA at Fenway. All with the Rays.

This places him on that short list of players, who, when you first see them in a different uniform, makes you want to rub your eyes and adjust the dial on the set.

When Boston fans think of players who never looked quite right in different laundry, there’s a gold standard. That would be Bobby Orr, whose brief, halting shifts with the Chicago Blackhawks in the last days of his otherworldly career are as horrible to remember as they were to watch. I’m told there was actually a pinball machine on the market showing No. 4 in his Blackhawks duds; we should find one and throw bricks at it, just on principle.

Another player who comes to mind is Carlton Fisk in a White Sox uniform. I covered his first game at Fenway as a visiting player, which happened to be Opening Day in 1981, and it just seemed … wrong. Yes, players come, players go, it’s a business — look, I get it. Still, we have eyes. We see, and sometimes we’re startled by what we see.

And sometimes the reverse happens: A player, even an iconic, Hall of Fame-bound player, changes his clothes so often that we become numb to it. Rickey Henderson immediately comes to mind. Though he had three different tours with the Oakland A’s over parts of 14 seasons, he also played for eight other teams. He could have shown up wearing an Adelaide Crows uniform of the Australian Football League and nobody would have noticed.

Remember Fred McGriff? I maintain that one reason his Hall of Fame candidacy has stalled is because he played for six different teams over 19 seasons, never for more than five seasons, and, thus, there’s really no organization to champion his cause.

Then again, that never stopped Reggie Jackson. Even after all these years it’s still hard to believe he only played five seasons for the Yankees. Or that Frank Robinson played just six seasons for the Orioles.

Back to David Price: I believe he’ll wind up having more career wins for the Red Sox than for any other team, the Rays included. So adjust the set a little, and soon everything will come into focus.