A solution is an n-tuple, but it gets confusing to call them vectors -- because then it's too easily confused with the difference vector.

Start with a base solution, modify it by a difference vector, cross the result with a target solution, and this creates a new trial solution.

See the linked diagram for more details.

http://www1.icsi.berkeley.edu/~storn/code.html

In DE,

• A parent vector from the present/current generation is called target vector,
• A mutant vector obtained through the differential mutation operation is known as donor vector and
• An offspring formed by recombining the donor with the target vector is called trial vector.
• In order to create the donor vector for each ith target vector from the current population, three other distinct parameter vectors, say X1, X2, and X3 are chosen randomly from the current population. The weighted difference of two vectors added into third.

I recommend you to have a look at the following articles:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.6764&rep=rep1&type=pdf

http://www.sciencedirect.com/science/article/pii/S0378779615001947

They refer to the individuals used in the mutation operator of the DE