Tensile stress is formally defined as the force exerted on an elastic object per unit cross-sectional area.
It has the same units as that of pressure, which are pascals (Pa). Now, it may even sound similar to the definition of pressure (i.e. force applied per unit area on a surface), but one must acknowledge the fundamental difference between the two.
Pressure is simply the amount of force you apply on a particular object on a unit area, with no focus placed on whether or not the shape of the object changes. But in the context of tensile stress, we acknowledge that it is indeed a tensile property - i.e. we require that the force exerted here has to stretch the object in question.
Tensile strain is defined as the extension per unit original length of the object. It is therefore simply a ratio without any units.
From the name, it is evident that this too is a tensile property, and for good measure: conceptually speaking, tensile strain is simply a measure of how much an object deforms due to a tensile force.