Tender has many meanings, depending on the context.
A "tender caress," that Michael mentions above means to gently (or softly) stroke something or somebody - for example your child's hair. A "tender embrace," is a hug.
But if a person is "feeling tender," it might mean that they have a hangover (they drank too much alcohol the night before) or it might mean that it is easy to upset them at the minute, due to events in their life.
If a wound "feels tender," then it is painful to the touch.
Unlike gentle, tender can also be a word with a completely different meaning - "to tender," means to make a bid to provide a service (it is something that a company does and is a competitive process).
Somebody mentioned meat above. We do, indeed, describe meat as being tender if it is soft.
We also have the verb "to tenderise," which means to make something more tender (soft) - it is used with meats or other foods (for example the food that babies eat).
Gentle is much more limited in meaning. A person or their actions can be gentle. A person can also be said to have a "gentle voice," if their voice is relatively quiet and pleasant to listen to.