Android - What's the difference between Data and Internal Storage?

Two relevant aspects before answering your specific questions :

• You are planning to install a new ROM

• The device is going to be with you so you are not bothered about wiping all personal traces ( like you would be if you are planning to sell)

• See What should I wipe in TWRP? from official TWRP help . That would take care of your needs for installing a new ROM

If you are switching ROMs (changing from one ROM to a completely different one) then you should perform a factory reset. A factory reset wipes data and cache (which includes dalvik cache). A factory reset will also wipe sd-ext and android_secure if your device has those items. 99% of the time, this is all that you need to wipe and you only need to do it once, not three times as some people would lead you to believe.

(Emphasis supplied)

factory-reset is equivalent to Wipe data,cache, dalvik. It will not remove your pictures . See Firelord's answer which has other useful references as well

...Factory Reset would remove everything under /data (excluding /data/media which serves as emulated storage available through /sdcard as internal SD card)...

• What's the difference between Data and Internal Storage?

Data is what is contained in the / datapartition. Internal storage world refer to the entire device directory structure and what is contained in them as well

• See What happens when I wipe the internal storage of a device using TWRP?

• Also TWRP help explains further

....you may have options for wiping internal storage, external storage, sd-ext, android_secure, and/or an option for formatting data. There's almost no reason that you would ever need to use these items....

(Emphasis Supplied)

The existing two answers are nice, but there are two things which are not quite correct in how TWRP handles and calls the different wiping options.

1. [This statement is wrong]: "Internal storage world [sic] refer to the entire device directory structure and what is contained in them as well."

   Instead, the term "Internal storage" as used by TWRP refers to /data/media.

2. [This one is also incorrect]: "On the other hand, Internal Storage is actually the storage where your other data are saved, such as music, photos, videos, other app data, downloads, etc., and is usually stored on /storage or /sdcard."

   More correctly, "Internal storage" is actually stored at /data/media (indeed it is usually mounted at something like /storage/emulated/... and /sdcard as well).

Source: https://twrp.me/faq/datamedia.html