Tissue culture is the in-vitro culturing of plant cells, tissues, or organs in an artificial nutrient medium, in controlled aseptic conditions. Example tomatoes and sweet potatoes.
Grafting is a method of artificial vegetative propagation in plants in which the root bearing part of a plant (stock) is joined with the stem or bud (scion) of another plant. Grafting is done for plants whose seeds have longer dormancy or to get seedless fruits. Example, Mango and Guava.
Stem cutting is a way of asexual reproduction in which a part of the stem of a plant is cut and planted in the soil and they develop adventitious roots. Soon it grows into a new plant. Example rose.
Layering involves burrowing a part of the stem under the soil while still being attached to the parent plant. The point of the stem which touches the soil produces adventitious roots and detaches from the parent plant to form a new plant. Example in strawberry.