If your carpet meets a new type of flooring whose height isn't the same as that of the carpet, use a combination threshold and tackless strip. Attach the threshold to the floor, and stretch the carpet over it as you would normally attach carpet to a tackless strip.
A step-down threshold is used when the new floor is higher than your carpet, as might be the case when installing carpet next to thick tile. This type of threshold is screwed down through the carpet and angled so that it can provide a smooth transition from one height to the next.
Another option when installing carpet next to tile is to butt the carpet against the tile and place a marble threshold over the edge. Marble thresholds typically cost about $10 and are applied with construction adhesive.