Memory
Phone memory is very fast storage, typically 1GB to 4GB.
Apps are loaded into memory when they are started. Most apps are limited to how much memory they can use by the Operating System.
Typically, memory is a chip (e.g. a 4GB DDR4 chip) connected to the SOC (System On a Chip). Generally speaking, memory is reported as total and available. Note: This is the total memory that the Android operating system can use, and is lower than the actual physical memory on the device. Some of the physical memory has fixed allocations and is set aside for other functions such as the GPU (graphics), the radio baseband CPU (cellular network functions) and DMA buffers (hardware subsystems).
Google suggest you leave apps open (consuming memory) and let the Android Operating System manage the memory. This results in faster switching between apps. While this generally makes sense, it will mean that your phone will have a smaller amount of available memory and Android may close background apps as the active app requests more memory. Generally speaking, I like to manually close apps I know I am finished with. Using “task killer” (cleaner) apps will, of course, free up memory, but will make it slower to restart an app that would have otherwise already been loaded into memory.
Storage
Phone storage is fast storage (but much slower than memory), typically 8GB to 256GB.
Apps are installed onto storage (where they remain even if the power is switched off). For security reasons, most apps are limited to what storage they can access (for example, one app typically cannot access storage used by another app).
Typically storage is a chip (e.g. a 64GB Universal Flash storage chip) connected to the SOC (System On a Chip).
Many phones provide a storage clean up tool to free up space. Examples are Settings -> Device maintenance (Samsung) and Settings -> Storage -> Free up space (Google Android 7.1).