Why are there different kinds of stitches or sutures?

Different healing. Sutures are used to help approximate soft tissues. Different soft tissues require certain healing times (skin, mucosa, muscle, tendon) therefore it is key to have sutures that last different times. The biggest distinction is permanent versus absorbable sutures.
Different needs. Similar to the variety of fishing lines required for different application. Physical considerations such as the strength required, location of use, condition of tissue, durability, or tissue reactivity all figure into the decision process your surgeons exercise while performing your surgery.