That is actually NOT how I know the terms and see them used (generally--they tend to get mixed up here on the DIS). My understanding is that helicopter parents tend to do far too much FOR their children. Either out of misguided love, or fear, or some belief that their children are not that capable, or because they think it makes them look like a good parent (or who knows what other reason

) they hover around their children and do all the work for them so that the child never really learns and grows. On the other hand, parents raising snowflakes treat the child in such a way as to give the child the belief that s/he is better and more important than everyone else and that every day rules should not apply to him/her. Some parents are both helicopter and snowflake makers, but many are just one or the other.
For example, lets pretend we have a family with a 5 year old child at one of those steak houses where you get buckets of peanuts on the table. Here are two very different scenarios:
Helicopter scenario: Mommy (or Daddy, but I will stick with all female genders to make my typing life easier

) lifts little future teacup (FT) into her seat rather than "risk" FT getting hurt climbing into the booth. Mommy shells peanuts for FT. Mommy orders for FT because FT is "too shy

" to speak to the waiter herself. When FT needs to go to the bathroom, Mommy escorts her, helps her with her clothes (not because FT has any motor skill issues but because Mommy has never taught FT how to do it herself) and hold her up to wash her hands (even though she can reach the sink) and helps her scrub them well enough then opens the door FOR FT with a paper towel before returning to the seat and lifting FT up again. When dinner arrives Mommy cuts all of FTs food into bite sized pieces, tucks a napkin in at her chin and hold the drink glass for her to avoid spills.
FT may well be very polite and sweet and in no way distrub any other diners.
Snowflake Scenario: Little Snowy climbs into her seat over the back of the booth by first climbing into the (occupied!) booth next to it. Mommy thinks this is so adorable--see how strong and active and outgoing Snowy is?. Snowy loudly shots "BAM!" while smashing the peanut shells. Again, Mommy thinks this is supremely cute. When it is time to order Snowy shows off by telling the waiter 50 odd facts that have nothing to do with the menu before finally ordering--holding up everyone else in the section during a busy Friday night. Mommy praises her daughter for being so smart and outgoing. When Snowy has to use the restroom Mommy goes with her to tell all those mean ladies who are waiting in line that Snowy is only 5 and has to go right away without waiting. When the food comes Snowy Shouts loudly to her parents about what she does and does not like and dumps the side dishes she dislikes onto the table and floor. Mommy complains that the waiter should have told Snowy that the pasta would have green herbs on top of it. Snowy enjoys making lost of bubbles in her drink (loudly) and flicking the liquid off the end of the straw at the patrons near her. Mommy is mad at the mean people who keep giving Snowy nasty looks when droplets of milk/spit land on them.
As the FT grows Mommy will likely be way too involved with her social life and her school life. Mommy will see herself as always being on top of things but she will really always be interfering with things. If FT breaks a rule at school Mommy is likely to call or email the teacher herself (even in highs school) to explain the issue instead of just giving FT some ideas of how she could handle it herself. If FT argues with another kid Mommy will be on the phone with the child's mother figuring out how they can get the kids back in a good place. When FT wants to babysit, Mommy will line up the jobs for her. Mommy will remind FT of due dates for every assignment, make sure FT always has everything she needs (AND RUN FORGOTTEN ITEMS TO HER always NO MATTER WHAT, Etc.)..
As Snowy grows Mommy will continue to defend her atrocious behaviour as sweet/adorable/precocious/special. . . When Snowy breaks a rule at school Mommy will be in the principal's office explaining why Snowy should not be punished. If she argues with a friend Mommy will tell her she is so much better than her friends that they are just jealous of her. When Snowy wants to babysit, Mommy will tell her she is too good to take care of other kids all day and give her a huge allowance instead (or set her up "working" for Mommy at an easy job for huge pay to feel good about earning her way). When Snowy forgets a due date or material for class Mommy will call the teacher to tell them they have to understand that Snowy just has too much on her plate and they cannot penalize her.
I can understand picking such a name on a parenting forum (since that is what the forum is about) and then even keeping it as one spreads out in the internet. Sort of like I am still NHDisneylover even though I have not lived in NH in almost 2 years (when I registered it was just for a cruise meet thread and I was just trying to come up with something for that--it is Disney related because this is a Disney board). Now I have that same name in two other places just because it has become my internet ID. I wish I had realized when I first registered that I would be more and more drawn into the internet and then I would have chosen something more ME.
However, I agree I have never understood people who really do seem to identify that way all the time--they have XXX's mom as emails, as licence plates, etc. What do they do and WHO are they when their kids grow up?