**INSTRUCTION SET:**

Processors are made of semiconductor dies, usually electronic-grade mono-crystalline silicon. They don't know English or any other human language, they understand only `0` and `1`. So the designer of processor tells us in what sequence of zero's and one's we can instruct that specific processor. This numerical language of instructions is standardized as `Machine Language` and the set of machine instructions is called `Instruction Set`. A processor can act upon only specific type(s) of instruction set. 
Instruction sets can be 8/16/32/64-bit (defines how many instructions a processor can process at a time), last 2 being the common one these days.

**WHAT IS SoC?**

A System on Chip (SoC) is a small circuit that includes processors along with other components such as GPU, RAM, Flash/eMMC (equivalent of HDD or SSD), WiFi and bluetooth module, USB connectivity, UART (serial ports), JTAG (a very lower level serial communication protocol), GPS, modems (for cellular connectivity) and possibly others.

**32-BIT VS. 64-BIT:**

A processor can be 32-bit or 64-bit. It depends on SoC manufacturers what they want to build with their embedded system e.g. Snapdragon can be 32-bit or 64-bit. 32-bit ARM processors were improved for performance and new features were added from version 2 to version 7. 64-bit support was introduced in ARMv8.

To find out if a device is 32-bit or 64-bit, you need to check out specifications of its SoC (which you can see e.g. from https://gsmarena.com) and then of its processor. For instance if an SoC contains `Cotrex-53` processor such as [Qualcomm Snapdragon 625 (MSM 8953)][4], it's evident from [technical specifications of Cortex-53][5] that it's a 64-bit ARMv8 processor having full backward compatibility with 32-bit ARMv7.

On-device processor/SoC information can be checked using some third party app as you have mentioned, or directly from CLI: `uname -m`, `cat /proc/cpuinfo`, `cat /sys/firmware/devicetree/base/model` etc.


 [4]: https://www.qualcomm.com/products/snapdragon-625-mobile-platform
 [5]: https://developer.arm.com/products/processors/cortex-a/cortex-a53