Is permissible stress and tensile strength the same?

First thing to decide is if you mean tensile strength as in your title or tensile stress as your post implies.

Tensile stress refers to a type of stress.
Strength refers to the maximum possible stress of that type that can be applied without failure.
So tensile strength refers to the maximum possible tensile stress, at which point the subject fails.

Permissible stress refers to an amount of stress that will not cause failure.

You should look up 'factor of safety.'

This is the ratio of the strength to permissible ie maximum to permissible and is usually in the range 2.5 : 1 to 8 :1.

 

section 7.5 here for instance provides various safety factors.

http://nptel.iitm.ac.in/courses/IIT-MADRAS/Machine_Design_II/pdf/2_7.pdf [Broken]

You should note that such factors in modern design are compound factors and are called load factors.
Modern design also provides factors applicable to the strength of a material. The strength used is known as the 'characteristic strength' and is measured according to some standard scheme.

Edit

Please note further that you either apply the safety factor to the stress to achieve a safety factor and use the actual nominal loads.
This is the older simpler method called the permissible stress approach.

or

You apply the safety factors to the loads and material properties but use the actual stresses calculated.
This is the more modern, more complicated method, known as limit state analysis.

You do not apply both.