What Anole says is all pretty much true. There are four basic classes of C-Band circular feeds that I've seen:
1. Dual polarity units with a removable dielectric slab. As Anole says, you have to put the slab in to receive L&R and take it out to receive H&V. One can buy these slabs separately, but I wouldn't expect a perfect match. Inexpensive.
2. Single polarity and orthomode units with a fixed 1/4 wave plate. These should offer the best reception, as those with dielectric slabs generally lose around 1 dB and are prone to increased cross-polarization. These tend to be fairly expensive.
3. Corotor-style feeds with a dielectric insert. The performance is pretty much like #1, however by aligning the slab either in H or V and rotating the pickup over a 135 degree range, you can have H&V and L&R and leave the slab in all the time.
4. Motorized feeds with a fixed 1/4 wave plate (I think). Similar in performance to #2. Instead of rotating the pickup, part of the feed is rotated. It may be able to do both H&V and L&R but I've never seen one in the flesh. Very expensive.