Difference between EOT and EOF
Generally, EOF isn't a character; it's the absence of a character.
If a program runs on a terminal in canonical mode with default settings (i.e. a plain C program that just uses stdio), it will never see the ASCII character EOT. The terminal driver recognizes that character and creates an EOF condition (which at the low level is a 0 return value from read()). The stdio library translates that EOF condition into the return value that is appropriate for the function in question (the EOF macro for getchar(), a null pointer for fgets(), etc.)
The numeric value of the EOF macro is of no relevance anywhere but in the C library, and it shouldn't influence your understanding of the meaning of the EOF condition.
EOF in the context of C is just something that cannot appear in a file. EOT is an ASCII character that historically signalled the end of a message (and is a special character in UNIX terminals that means end of stream when it appears in user input only), but it CAN appear in files, so using it in C to signal the end of a file would be a terrible idea when reading binary files!
EOT is one of a number of control characters used by seerial devices. There are a number of other control characters which are related to transmission of data over serial lines or storage of files on a serial source like paper tape. These include characters such as SOH, STX, ETX, FS, RS, GS, and, US. Additional control characters are used for transmission control and error correction.
On a serial connection an EOT (End Of Transmission) character indicates a desire to end the transmission. Serial connections are usually accessed using a file driver. When the serial transmission ends, the file driver reports this as an EOF (End Of File) condition.
EOF is not a character. getchar() returns an integer. A valid character while will have a value in the range 0 to 255. The value of -1 is often used as false/invalid/fail indicator on Unix/Linux. (Actually a non 0 value, as there are any number of reasons not to succeed, but usually only one success case.) When getchar() returns -1 it is clearly not returning a character. However, if you store the output in a byte, you won't be able to distinguish EOF from the DEL (Delete) character.