Bonnell coils:

The oldest and most common. First adapted from buggy seat springs of the 19th century, they are still prevalent in the majority of mattresses sold in the Canada  Bonnell coils are hourglass-shaped, and the ends of the wire are knotted or wrapped around the top and bottom circular portion of the coil and self-tied.

Parker's Bonnel Coil Models:

Two Sided - Hotel Deluxe Firm
Two sided - BOWEN Plush

Marshall "pocket" coils:

Each wrapped in a fabric encasement and usually are tempered . Many people believe that this design reduces motion transfer.  The best pocket coil beds are foam encased.  Pocket coils are used by Simmons in their Beautyrest beds.

Parker's 800 to 816 Individual Pocket coil Models:

Tight Top - BODY  FORM  - Firm
Locarno - Thin Pillowtop
Qualicum - Thick Pillowtop
Dundarave - Thick memory foam  pillowtop
Pillowtop Ambleside
High/Low configuration Pocket Coil Marpole

Offset coils:

Designed to hinge, thus conforming to body shape. They are very sturdy, stable innersprings that provide great support. Offset coils are used by Sealy in their Posturepedic beds.

Parker's 672 Offset Coil Models:

Jericho Euro-Pillowtop

Continuous coils:

Work by a hinging effect, similar to that of offset coils. In a basic sense a continuous coil is simply that, one continuous coil in and up and down fashion forming one row (usually from head to toe) of what appear to be individual coils. The advantages of these types of coils is that they are very firm and supportive for heavier people. Serta uses these types of coils in their Perfect Sleeper beds

Parker's 720 Zoned Continuous Coil Models:

Two sided Mayne - Plush
Kerridale   - Ultra Firm
Kitsilano   - Plush