Is there in fact an in-game scoreboard I can bring up during the match?

No, there's is not. In fact Jeff Kaplan himself has stated in an interview:

So we we basically stopped displaying any form of scores, kills, deaths because it really wasn't telling the story of who was doing their job properly to win or lose as a team. And really, what it's all about is, "Did you win or lose as a team?" None of that other stuff really matters at the end of the day.

You have some form of knowing if you were one of the top performers of the game by the medals and upvotes you get.
You can also view your performance in the "Tab Menu" or tab-screen. See the next section.

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Are people talking about a different screen when they mention the tab-screen?

The tab-screen is not the hero select screen. Here's an example of a tab-screen:

As you can see there are some of your stats there that you can check but you can't compare them against any other player. As I've explained in the previous section, this is intentional to promote team play.

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Bonus

During development, Overwatch had indeed a scoreboard that has since been long removed.
The scoreboard used to look like this:

Redditor SpriteGuy_000 has done some extensive testing, and according to his spreadsheet these are the things you can be commended for.

All Heroes

• Eliminations (% Kill Participation)
• Objective Time
• Damage Done (% of Team Damage)
• Gold Medals Earned (Total Medals)
• Total Medals
• Objective Kills (Eliminations)
• Best Kill Streak (Eliminations)
• Teleporter Pads Destroyed (Enemy Teleporters Placed)
• MVP (% of Match on Fire)
• Melee Final Blows (% of Final Blows)
• Environmental Kills (Eliminations)
• Solo Kills (Eliminations)

Bastion

• Recon Kills (Eliminations)

D.Va

• Mechs Called (Mech Deaths)

Genji

• Damage Reflected (Deflection Eliminations)
• Dragonblade Kills (Dragonblades)

Hanzo

• Doesn't appear to have any unique commendations

Junkrat

• Players Trapped

Lúcio

• Healing Done (% of Team Damage Taken)
• Sound Barriers Provided (Sound Barrier Casts)

McCree

• Fan the Hammer Kills (Total Eliminations)

Mei

• Enemies Frozen (Total Time Frozen)
• Damage Blocked

Mercy

• Players Resurrected (% of total deaths)
• Healing Done (% of Team Damage Taken)
• Defensive Assists (% Kill Participation)

Pharah

• Rocket Direct Hits (% of Rockets Fired)
• Barrage Kills (Rocket Barrages)

Reaper

• Souls Consumed ()
• Death Blossom Kills (Eliminations)

Reinhardt

• Damage Blocked

Roadhog

• Self Healing (% of Damage Taken)
• Enemies Hooked (% Hook Accuracy)

Soldier: 76

• Helix Rockets Kills (Eliminations)

Symmetra

• Players Teleported (% Teleporter Uptime)
• Sentry Turret Kills (Eliminations)
• Shields Provided (% Shield Uptime)

Torbjörn

• Armor Packs Created (% Armor Uptime)
• Turret Kills (% Kill Participation)

Tracer

• Health Recovered (Recalls Used)

Widowmaker

• Infra-Sight Uptime (Recon Assists)

Winston

• Damage Blocked
• Jump Pack Kills

Zarya

• Projected Barriers Applied (Damage Blocked)

Zenyatta

• Transcendence Healing (Healing Done)
• Healing Done (% of Team Damage Taken)
• Defensive Assists (% Kill Participation)