Binary data / binary file mostly refers to a file or string of bytes in which some coding is used that is not (guaranteed to be) just text. The term has a sense of not being trivially human-readable. (Note that has no direct relation to binary in the on-off, base-two sense)
If a file or (byte)string contains only text (particularly if in a common coding like ASCII, ISO8859, UTF8) it would often be called plain text.
A bytestring (sometimes binary string) is a string (in the programming sense) that can contain any value (is not a string of only (readable) characters, that there is no termination value, implying that the length is stored separately. (not necessarily so in C strings).
A string in the wide sense refers to a string/array of values but (since we have words like array and list) it usually refers specifically to a string of readable characters (unless terms like bytestring are used).
A binary often refers to a program in executable (and often compiled) form.