Tickle is used for two sensations.
The first is the very light touch, for example with a feather, or from an insect walking on your skin. This is nearly always uncomfortable, and doesn't make you laugh. It is possible to give yourself this sensation.
The second is a heavier touch, usually with fingers. This does make you laugh, and may be enjoyable depending on the context. We might tickle our children or a lover to make them laugh, but too much tickling can be torture. It is generally impossible to create this sensation in yourself.
Tickle can refer to both these sensations. There are two very technical words for these, but I'd never heard these words before researching this answer, so they cannot be used except in a research paper in psychology.
Pat mean to gently tap with your open palm. Stroke means to rub gently with your hands. Typically you pat a dog, but stroke a cat. Neither act would be described as tickling.
Caress is a gentle and loving embrace, touch or stroke. You caress a lover's body, or a mother could caress her baby's cheek.