Let me clarify this, and some other things.
The <=$60 converter boxes, like all digital TV tuners, do have the ability to receive HD channels. They just downconvert the HD to SD on output. This is an important point, since a lot of programming is only being broadcast in HD, but will still be watchable on SD-only sets. E.g., all of the major broadcast network affiliates in NYC (CBS, NBC, FOX, ABC, MyNetwork, CW, PBS) are broadcasting in HD *only*. If you are concerned about being able to see the full HD resolution on an HD set that doesn't have an up-to-date digital tuner, then the cheap converter boxes won't do it for you. But if you're only concerned about being able to receive all of the channels in SD, including the HD ones, then any digital tuner will do.
As far as the distinction between "digital" and "HDTV" antennas, forget it. It's a marketing scam. Any antenna capable of receiving a digital TV signal will give you HD, whether it's marketed as HD or not. A digital TV signal is a stream of bits. The bit rate is fixed and determined by the 6MHz bandwidth. No matter whether the frequency is carrying an SD channel, an HD channel, or several subchannels of HD and SD combined, it all has to be compressed down to 19.38Mb/s. The tuner receives the bit stream and picks out the bits that relate to the subchannel you're trying to receive. Either you receive the whole bit stream or you don't. Whether some, most, or all of those bits are carrying an HD picture has no effect on the antenna's ability to receive the bit stream.