Generally speaking, the Star printers will just show TSP100 on the front of the actual printer but those are the model numbers; it is kind of confusing. Feel free to share a link or two to the printers you’re viewing, I’d be happy to confirm. 
The STAR MICRONICS SM-T300I is also a light weight receipt printer. But it’s very durable and rugged. It’s also Apple MFi certified for iOS phone and iPads. It also works with Android and Windows. It’s been tested to take a little bit of beating and is used by people who are outside a lot. Having said that the price is higher than other printers. If you need something rugged, this device may be the one for you. But if you don’t. You will want to look at something else as this device can get expensive. The SM-T300i is easy to use. There is a well written and very detailed user manual. The user manual gives details on how to configure the receipt printer and how to load paper. Here is a link to the Star Micronics SM-T300i User Manual.
Have not purchased this printer, but wanted to let people know that this is not the only printer that will work with Square. I have two Star Micronics printers, one Ethernet and one Bluetooth and both work fine with the Square app for iPad. I also have Ethernet based cash drawers that connect through the printers and those works just as well. This probably has the easiest set up, but it is not the only way.
The printer that Square supports is one of the largest used brands in the receipt printer market.  They are not getting kickbacks on printers as the printers are sold by hundreds of places including Amazon, and the buyer doesn’t know you are buying it to print with Square as the printer is also used by 100s of other POS systems. More printer options would always be better, but as this is one of the industry standard printers it only makes sense they support it.
NOT FOR USE WITH SQUARE STAND! If using a Square Stand consider the Square Stand Starter kit which has a printer that plugs into the stand. The printer in this kit must be plugged into your router.    
A printer-driven cash drawer must be connected to an receipt printer to open automatically. Otherwise you’ll need to manually open the drawer using the cash drawer key. A USB cash drawer (requires Square Stand) will open automatically when connected.
Connect supported receipt printers, cash drawers, and bar code scanners to the Square app on the iPad. If you have any connectivity issues after following the steps below, learn how to troubleshoot your hardware.
Amounts shown in italicized text are for items listed in currency other than U.S. dollars and are approximate conversions to U.S. dollars based upon Bloomberg’s conversion rates. For more recent exchange rates, please use the Universal Currency Converter
USB 58mm POS Thermal Dot Receipt Printer Set Electronic POS Cash Drawer. POS Printer Support cash drawer driving, connect the cash drawer with RJ11 Connector Cable(RJ11 cable not included). Compatib…
Connect your Square Stand with a compatible iPad and recommended hardware accessories to help run your business. Before purchasing a Square Stand, make sure you’re using a supported iPad. You can identify your iPad model on Apple’s Support site.
Learn more here.

Impact printers only print order tickets for a kitchen. They’re not affected by heat and can withstand warm environments. They require heat-sensitive paper and won’t work with non-thermal, receipt printer paper. 
Star Micronics TSP100Receipt Printer is the first All-in-One receipt printer on the market today!. The advantage of TSP143LAN Receipt Printer is evident for applications such as retail, restaurants, and convenience stores. TSP143LAN Receipt Printer is provided with all standard operating system drivers (Windows, Linux and Mac) and specialty drivers such as OPOS and JPOS. The printer is also directly supported in Square Register. Star has also included a number of embedded simple utilities that will enhance Retail or Hospitality CRM in POS applications and therefore make the entire experience simple. These printers come complete with every thing you need including printer, power supply, Ethernet cable, wall bracket and a roll of thermal paper.
Square Register Star TSP100III Thermal Receipt Printer with Auto-Cut, Ethernet Interface 10/100BaseT (LAN), Internal Power Supply, Includes TSP143IIILAN, Power Cable, Ethernet Interface Cable, Mounting Kit, Paper Roll, Dark Grey Color – TSP143IIILAN GY US – 39464910
It has 5 bill trays, 5 coin trays and a bill entry, keeping your money organized and largely improve your working efficiency and accuracy. Electronic Cash Drawer 1 Cash Drawer. Only the cash drawer is…
We really like the Apple MFi certification with the auto connect feature. We also like the small footprint of this receipt printer. Overall this is one easy and fast printer to setup. The Apple MFi makes it real easy. You just turn the printer on within range of your iPad.
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Thermal Printer Features: 100% brand new and high quality Suitable for all types of commercial retail POS systems Light in weight and smart in shape High-quality printing and low cost Low noise and h…
I do appreciate your post though and I wanted to let you know that we are working to provide support for more printers and your feedback is welcome! For example, we recently launched support for several Epson printers which can be used with Square on iOS devices (the full list of printers is here). 
Edit to say that the network issues I mentioned were tied to the wireless router we were using. Replaced that piece and the printer started working great. I still recommend purchasing as a package for better price and customer service, but not a bad piece of equipment.
EOM-POS Heavy Duty Cash Register Money Drawer + Mounting Brackets for Under Counter Installation. Compatible with Square Stand [Receipt Printer Required]. Built in cable to connect to receipt printer.
POSGuys.com Square Stand POS Kit The Square Stand point of sale kit leaves the guess work out of purchasing compatible hardware that is reliable and looks fantastic with the Square Stand. These kits are designed for customers who need every part to just a few pieces to make a complete Square Stand register.
The new Square Contactless and Chip Reader is included so you can accept every way your customers want to pay. Place the reader in the dock, connect the dock to the USB hub, and you’re ready for business. Accept magstripe cards, chip cards, and NFC payments like Apple Pay.
This is one of the more common receipt printers used with Square Payments. It generally costs less than $200. It come in white and black color. It has an auto-cutter to slice receipt paper for you. It uses thermal paper so you never never need to fill it with ink. It is generally easy to maintain and add paper when you need it. So this is a printer that works well in a wide variety of environments. However, if you are in a kitchen or some area where the air is moist you may want to get an impact printer as thermal paper does not work well in moist environments where there is little ventilation. ​Here is the user manual for the Star Micronics SM-S230i.

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