You can buy the same bike at different stores (see for example the Schwinn Discover, here, here, and here). Does the place where you buy the bike from matter in terms of what parts they put on it? Or is the only difference in the assembly?
It matters in many ways where you buy the bike from. If you're buying online, then the parts will most likely be the same, although you should be careful to read the specs. Some online (brick and mortar as well) shops will have overstock bikes from previous years and the parts will be different from the current model year.
If you buy from a local bike store, then it starts to make more of a difference where you shop. Many shops will offer free tune-ups for a year or two, and some others will offer free tune-ups for life. What's included in a "tune-up" can vary from store to store. Some shops will include a free fitting of the bike to make sure it's properly set up.
Every actual bike shop, and dedicated sporting goods store that I have been to has, at the minimum, given the bike a the bike a safety check before they actually hand it over to you. I even got this once for a coaster bike (the kind with no pedals/drivetrain) when I bought one for my 3 year old.
This is to ensure that the bike is in safe operating condition and to ensure that things are working well. Problems can arise between the initial assembly and when you purchase the bike and they want to ensure that you will be safe and have a good experience. Stuff like this often isn't done at places like Walmart or Amazon. Often they will assemble the bike and not even give it a test ride to ensure things are actually working properly.
The difference is the support you get afterwards. If you buy a decent (non-BSO) bike online, you're generally on your own for support unless you take it to a bike shop and shell out some money. They often won't let you swap out the bike with another size if it doesn't fit you properly either.
On the other hand, if you go to your local bike shop, many of them will do adjustments on the bike for free for a while, and if it doesn't fit, they can help swap out the model for you for something that does fit.
Another point is the assembly - not everyone is as careful as everyone else when they put together a bike, which is why even the BSO's at Walmart typically don't operate as well as they should when you get them from the store.
Sometimes there are different trim levels of a bike with different parts, but are usually clearly demarcated on decent quality bikes. Generally, for the same trim level, the parts will be the same as they're spec'd that way from the manufacturer. (An exception being things bought from some online retailers like BikesDirect, which does substitute similar parts on a given model possibly from different manufacturers). On BSO's, this is not necessarily the case.
In this case, the bike is really a high end BSO, so you may get some slight variations between dealers, but they should all be essentially equivalent parts.
On a bicycle the store is the final point of assembly. The bicycle arrives in a box unassembled. So yes it makes a difference.
The parts are in the box so unless you swap out some part you will get the same parts.
I bought a high end bike at a general sports store where they also sold ski and camping equipment. It took me hours to get that bike running correctly. They just put the parts together and did not tune it up. I knew what I was getting but the price was right.
A high end store will even do stuff like put the wheels on the stand to verify they are true. Back before pre-stretched cables they would stretch the cables.
On mail order you will typically get what is call pre-assembled.
Reading your question again.
Does the place where you buy the bike from matter in terms of what parts they put on it?
A bike from a manufacturer will (typically) have a build kit and seller should not deviate from that. If they are subbing parts then that is just plain wrong. But what you might get is a prior year that did not have as good of components. Or before a frame construction improvement. Or a model number / name that is downgraded components that you might not have picked up on. On the Internet you will see these moved at good prices. You just need to ask the right questions. A LBS is more likely to be up front with this is a last years model. You should look for posted build kit and if it says component may be subbed then ask them straight up what components are on the bike you are selling.
Your three links are all shipping. I would go Amazon just because I know they have an excellent return policy. That is a lower end bike and is going to have lower end parts. None of those links even state a specific build kit. If it just says Shimano you need to be prepared for the cheapest Shimano. I would check for sales at you LBS.
If you take cycling seriously, the relationship that you have with your LBS is very important. Everyone at my LBS knows me and I know them. Having purchased many high-end bicycles over the past 20 years from two bike shops (depending on where I lived), I get first-rate customer service anytime I walk through the door. The owners, sales staff, and my favorite... the mechanics, know how I ride, what I appreciate in a bicycle, and what I expect from them. We click. Over the years, my LBS has suggested new bikes, frames, and components to me, based on their observations of what and how I like to ride, that kept my enthusiasm for cycling peaked. They have also called me anytime a factory recall affected me, my wife, or anyone I may have traded with. If at all possible I ride every day, and I arguably ride the best road bikes on the market because I swap, trade, and ride with other cyclists I met through my LBS. My LBS has also kept my 20 year old mountain bike purring through mud, rain, ice, and neglect. I love my LBS.
way back in the 70's I bought my first bike at a 'bike store' and thought having to lean to a side was the norm. Years later, having much more experience, I found out the frame was misaligned. What got me is this store which was supposed to be catering to bike enthusiasts would put out something like that and sell it at a premium price.
If a frame is misaligned there isn't much you can do. Any experienced shop owner would reject it instead of trying to sell it to an unsuspecting customer.
I modified the bike by gearing it up to 15 speed from 10 speed. but not in the way most people do. whereas most gear down to make it easier on hills, I went the other way and got a bigger sprocket on the front. I also moved the shift levers to the handle bars (shimano). I know people say they are slow but I like the comfort. Switched to cloth wrapped handlebars as well. stripped all unnecessary other stuff off the bike, but it was a circa '76 bike and weighed in around 30 lbs.
I did ride the bike on several century races for fun and experience but always had to sit to the side in the saddle.