I usually think of a bite being blood. BUT, it really is intent. It is whether they wanted to hurt you or did it just want to warn you or play or what. I have a full set of teeth scar from my BMF while breaking up a fight. I had on two long sleeved shirts and it still went through like butter and bruised and all. He was hoping to get his sister and obviously in that fraction of a second thankfully realized it was me. Broke up that fight VERY fast once mommy was bleeding.
So I have had dogs never even get me that I muzzle for grooming and I have had dogs draw blood but we are all friends later.
Reason and intent.

More times then not the skin is broken when the person being bitten jerks their hand/foot/etc away.

Very fortunately for me, I've only been bitten twice (by dogs...probably about 100 times by cats). Both times pretty serious bites, in terms of damage done, and pain. However, neither drew blood, just serious bruising. Both times by large pittys, while working at the Humane Society.
The first time, was accidental - I believe. The dog was totally obsessed with attacking blankets. I had a (thankfully thick) wool blanket draped over my arm, and someone inexperienced who shouldn't have been moving the dog around, had her by the leash. The dog leaped at my arm like a SchH dog to a sleeve, hung on and shook. No blood, lots of pain.
The second time was a new intake. He was 13 years old, and the owners had not told us that he had very painful throat cancer. I lassoed the dog through a small opening in the cage door. He seemed fairly indifferent so I opened the cage door. When he moved to come out, the leash tightened around his neck (I think very painful for him), and he jumped at my face. That moment was too close for comfort, for sure. I could hear his teeth crack down together, and feel the wind on my cheek. I instinctively put my arm up and pulled him down by the leash, but he grabbed my arm on the way down. Again, thankfully I had on a big Arctic expedition type jacket, as it was winter. He released my arm, and I tried to kick him back in the cage. Of course this is all happening in a split second - he spun around behind me and started jumping and biting me on the back. I backed up towards the cage, and luckily someone came by and slammed the cage door, knocking him off of me. Again, no blood, lots of pain. They decided to euthanize that dog the next day, due to his age, advanced cancer and aggression.
Both times, intentional or not, there would have been blood, if not for protective covering. But, I still considered them serious bites.
Actually, I have been nipped at a bunch of times at the vet by little nervous balls of fur, but never badly... but I have seen people lose nails to chihuahuas.

I agree, intent is important if it's your own dog biting you. Otherwise I don't let anyone not in the family play with my dogs so we don'e get any bites intended or not. My dog bit my neighbor but it wasn't reported. (He came in the yard when no one was out there) I haven't had a bad bite since I was about 12.
I'm surprised I wasn't afraid of dogs after having all these before the age of 13. Still love em-A lot more careful now
OK are we listing bites. My noteable bites.
GSD-Blood
Pitbull-no blood
Standard Poodle-Bad needed stitches in my back
Husky Mix-had on a parka bruised no blood
Chow mix-bruise

Here's the way we 'measure' it -
Level 1- Dog growls, lunges, snarls-no teeth touch skin. Mostly intimidation behavior.

Level 2- Teeth touch skin but no puncture. May have red mark/minor bruise from dog’s head or snout, may have minor scratches from paws/nails. Minor surface abrasions acceptable.

Level 3- Punctures ½ the length of a canine tooth, one to four holes, single bite.No tearing or slashes.Victim not shaken side to side. Bruising.

Level 4- One to four holes from a single bite, one hole deeper than ½ the length of a canine tooth, typically contact/punctures from more than canines only. Black bruising, tears and/or slashing wounds. Dog clamped down and shook or slashed victim.

Level 5- Multiple bites at Level 4 or above. A concerted, repeated attack.

Level 6- Any bite resulting in death of a human.

We don't count it as a dog bite unless there is a puncture or tear. the severity of the bite is determined by the color of the blood. Bright red, shallow bite, the fist aid kit is used and back to work. Dark red, muscle blood earns a trip to the ER. If we stopped for every nick and scratch we'd never get any work done.

DFrost

 Quote: David C.Frost

Dark red, muscle blood earns a trip to the ER.

Even if the puncture diameter is small? Why? Is such deep bite more dangerous?

 Quote: Ana Kozlowsky

Even if the puncture diameter is small? Why? Is such deep bite more dangerous?

Deep puncture wounds need special attention.

Bleeding might be low, but infection risk (including, but certainly not limited to, tetanus) is high.

I don't mean to answer for David -- puncture wounds from other instruments besides teeth also need special attention.

Thank you, Connie. I had no idea. I shall look into this further, just in case.

Yes I was told the small looking but deep puncture on my finger was much more dangerous than the nasty looking tear on my palm.

I was given tetanus, a shot of antibiotics, as well as oral antibiotics for my recent bite.

I was also told no peroxide, neosporin, or other typical wound care products because it can damage the tissue in the puncture and cause more problems.