Please see the attachment in the following useful link:
https://en.wikipedia.org/wiki/Tensor#cite_note-1
Tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors. Elementary examples of such relations include the dot product, the cross product, and linear maps. Euclidean vectors, often used in physics and engineering applications, and scalars themselves are also tensors.
I will try to answer, from the point of view of an engineer. In my response, I repeat what I wrote on the websites https://www.researchgate.net/post/what_is_the_difference_between_vector_and_tensor and https://www.researchgate.net/post/What_are_tensors.
For description of the tensor concept, the Cartesian coordinate system is assumed.
Physical Quantities, which are not dependent on this coordinate system, are scalars. Scalar is described by one number. Mass or temperature are scalars, for instance. On the contrary, some other physical quantities are defined with respect to coordinate system. These quantities are tensors (By the way, scalar is a tensor of rank zero).
Vector is a first rank tensor. For example, the force or electric field are vectors. For the given coordinate system, vector is completely defined by their three components. These components are perpendicular projection of the vector to respective axis of the system. In its description there is one index.
Second rank tensor is a physical quantity, which is defined by nine numbers, which form square matrix. In its description are two indexes. The number of indexes is equal to rank of tensor. As an example of second rank tensors, it can be considered resistivity (or conductivity) of stressed silicon layer, stress as well as strain.
Third rank tensor is a system of twenty-seven numbers represented as a cube of dimension 3x3x3. In its description, there are three indices. Tensor of piezoelectric coefficients is an example of third rank tensor.
Forth rank tensor is system of eighty-one numbers represented as a cube in 4-D space of dimension 3x3x3x3. In its description, there are three indexes. Examples: elasticity, stiffness, piezoresistivity, elastoresistivity as well as elastoconductivity.
In conclusion, we can say that the tensor is a physical quantity, which is described by a number of components, whose values are depend on the coordinate system. In this way, the vector is also tensor.