Will the pictures in "File Explorer" transfer over from the HDD to the SSD?
I'm not sure I understand the context of the question.
Are talking about dragging and dropping .vs. cloning the drive?
Any program that can copy files (File Explorer included) can do so between drives (regardless of their mechanical configuration) as long as both drives are connected. File Explorer in particular will usually miss hidden and system files so it isn't particularly useful for archiving. If you want to make backups of your important files, I'd suggest you use a bona fide backup program. Backup programs may catch information (like NTFS Alternate Data Streams; a Microsoft version of the old Mac Resource Fork) that File Explorer can't.
Pictures aren't special files from a backup or copy standpoint. They're treated no differently than any other file (i.e. .EXE, .XLS, .BAT, .ZIP, .RAR, etc.).