Generally, An external or " hardware interrupt" is caused by an external hardware module. Internal interrupts, or "software interrupts," are triggered by a software instruction and operate similarly to a jump or branch instruction.
Ref. – Interrupts
A Software interrupt is an interrupt generated by any computer's internal system.
Based on the above Wikipedia article, we should not assume that internal and software interrupts are the same.
A software interrupt is a type of interrupt caused either by a special instruction in the instruction set or by an exceptional condition in the processor itself. Typically, internal interrupts resist user changes and happen "naturally" or "automatically" as a processor works through program instructions rather than being caused by external events or network connections.
Now, refer to → Answer given in response to a question asked in Uttarakhand Asst. Professor Exam and we can notice specific differences between the terms “Internal interrupt” & “Software interrupt” in their application and how they are referred to.
The term “internal interrupt” seems to be used chiefly to refer to what are also known as exceptions: interrupts that occur in response to a processing error, such as referencing an invalid address in memory, division by zero, or similar error condition.
Ref.- Difference between Internal & software interrupt.
Software interrupts- A user program requests operating system services by executing the SWI instruction. This is an exception that causes entry into the Supervisor mode. A parameter field in the instruction specifies the requested service and is accessible from the Supervisor routines. (Hamacher-6th ed- pg 643)
So we can safely say that both internal and software caused by executing the program instructions are not the same.