Mattocks are used for loosening soil that is root filled. These have an axe-head on one side and a flat hoelike head on the other. Garden rakes are used to level and prepare seedbeds for planting. They are not meant for lawn areas. Garden rakes may damage the turf and their tines often become plugged with debris.
Lawn rakes handle lawn debris such as grass clippings and leaves.
They are best used with a sweeping motion like you would a broom. Hoes are used for cultivation and weeding. There are many types available. A general gardening hoe will work fine for cultivation and weed removal. Triangle shaped hoes are excellent for breaking into stubborn soil, weeding, and cultivation in tight spots.