The grounded (Type B) plug/socket is supposed to absorb large amounts of electricity and keep connected devices safe from surges. In (most of) the Americas, if you buy something like a mobile phone, shaver, tablet, hair dryer, etc. it would have a type A plug. Something like a desktop computer, vacuum cleaner, or lamp would have a type B plug. This is different from the UK where everything has the three-prong and everything is grounded.
The Type A output adapter will work in a Type A (non-grounded) or Type B (grounded) socket; the Type B output adapter will only work in a Type B socket. I'd say most sockets in the USA are Type B (accomodating both A and B plugs) but there are exceptions - for example hotel, hostel, gym, etc. bathrooms often only have a Type A and you may also find Type A in older non-commercial buildings or on trains, buses, planes, etc.
If he's travelling in the USA with "light" appliances like a phone, shaver, hairdryer, tablet, laptop, then he's probably best with a Type A output adapter. If he's moving and bringing things that use significant current like a desktop computer, vacuum, microwave, etc. he will need the B. It's sometimes said that a laptop should have a grounded (B) plug, but that probably depends on how much voltage it uses. I've been using a MacBook Air with a UK plug and a Type A adepter in the USA, Canada, and Mexico for about a year with a Type A adapter and no issues.