I've had people tell me that for boxing training purposes, wrestling shoes will do just fine. Yes, those types of shoes are similar to boxing shoes in terms of traction. But they are made for an entirely different sport. Regardless of whether a boxer is an amateur or a pro, it is preferable to have boxing shoes.
I would advise purchasing shoes from a boxing equipment company as opposed to a sporting goods store. Personally, I've never seen boxing shoes being sold in sporting goods stores. Most of those type stores hardly carry boxing equipment, let alone shoes for that purpose. Everlast, Title Boxing, Ringside, and several other like companies on line will have what you need, and they run sales from time to time.
Low top boxing shoes resemble regular athletic shoes, or "tennis shoes" as my siblings and I used to say when we were kids. A lot of them look very cool, and they come in all kinds of colors. But those shoes won't provide much in the way of ankle support. However, they will help with moving faster around the ring.
High top shoes help boxers who do a lot of pivoting and other fancy footwork. There is support for ankles and shins with those types of shoes. Regardless of whether the shoes are low tops or high tops, pick a light, but durable pair.
Just like when buying any other type of shoes, try them on first if you can. That's not possible when buying them online, so buyers should know their foot size very well. Feet are very important in boxing. Having a ill-fitting pair of shoes is not going to be very helpful while training or sparring, and especially during a regular fight.