Actual piercers will use a small, hollow needle to pierce the ear. It slices through the flesh and leaves a neat hole without causing trauma to the area, and heals the same as any clean wound if looked after properly.
Using piercing guns, like at Claire's, causes massive trauma to the skin and flesh as instead of a hollow, sharp needle, the ear is pierced with a solid and fairly blunt earring, forced through the ear at speed. This can cause a lot of scarring, and the ear will take longer to heal.
The needles used by piercers can be sterilised in an autoclave, piercing guns cannot be fully sterilised, meaning there is a higher risk of infection, even when using new, sterilised earrings.
The people who work in Claire's are given a day or so of training for piercing, and train by using the gun on teddy bears. Professional piercers study and train for months or years, and are certified.
The cleaning solution they sell you are really bad for healing too, you should only use saline and salt water to clean. They also now sell an 'accelerated healing' 3-week treatment, claiming the piercings will be healed and the earrings can be changed in 3 weeks. This is complete nonsense, you cannot speed up the body's healing process, and especially not with their crappy cleaning solution. Lobe piercings will take 6-8 weeks to heal to the point of changing the jewellery, no matter what you use to clean them, and changing the jewellery before this is really bad for the healing process, encourages more scar tissue to form and makes for a much higher risk of infection.
Yes, you can get your ears pierced at Claire's and have no issue, but it's still a bad idea. There are far, far more horror stories about ear piercings from Claire's than from actual, professionally trained piercers.