As I posted last, I am trying to "understand" the differences and if there is a difference? It has come up in our group discussions and it's not at all in a way that suggests anyone is less than excited for each others children. (I guess that's what I get for trying to post while my little kids are running around the room screaming and playing, things don't come out right.)

This particular mom has been involved in these discussions as the newer Moms try to sort out the potential giftedness of their child. We all try to understand the difference between parent driven and child driven learning. All wanting to understand the extremes on either side. I'm sorry if this came across wrong. I am taking offense to being jumped on about the question. I don't think I'm the first or the last parent to want to understand it.
I've googled the topic and can't find any resources to help answer our questions. I thought I'd ask the experts on this forum for their thoughts. I'm surprised by most of the reactions as it almost seems as though it's threatening to suggest the parents are directing the child's learning.
I think a lot of people here have been judged by others on the basis of what their children can do. I know I have. I have had a school district treat me like a pushy mom and then get very uncomfortable when their assessment tests proved that what I had been saying was right. The idea of judging another mom on her toy choices sort of falls under that umbrella.
However that wasn't what you were talking about. Your question is actually a very valid one. How CAN you tell between children that are being pushed and children that are gifted? For example if you run a group/school/whatever that only allows in gifted children knowing this would matter a lot especially if testing wasn't an option (age, funds, etc...).
I have worked with a lot of kids in my life and what I've noticed is that it's a matter of quality, not quantity. You can show any kid the alphabet often enough and they will eventually get it. You can show many/most gifted kids the alphabet a couple of times and they will have it down. Ditto for numbers, math, topics of interest, etc... The gifted kid will not only pick up the alphabet, but then point out the letters around the house or start to sound out words. When they are little there is almost an insatiable hunger to soak in more information.
Play tends to be different as well. Imaginative play often starts earlier and level of detail is much higher. There is often a great obsession with one or two topics at a time. They also seem to NEED more stimulation than other kids.
Example: Almost all kids can and will learn to read. Most kids start to sound out words and read low level readers through K-1. My son had a few sight words at 3, but then taught himself to read in one month shortly after he turned 4 and is now reading around 2nd/3rd grade level at 5 yrs old.
Unless you spend time with the children without the parents around it can be hard to tell gifted from trained. Anecdotal stories from the parent showing learning initiative on the part of the child (like the one above) are a hint. If you can observe the child playing with others of the same age who you know are on the normal development track, you can look for use of concepts more advanced than those of the playmate, more intricacy in the games, more imagination, more leaps of logic, etc... Also look for expressions of empathy and compassion beyond their age.
Hope that helps a little.