touch finger creates an empty file (or changes the timestamp of an existing file) called finger.
finger is an implementation of the Finger protocol, which is not used much anymore.
The finger program was written in 1971 by Les Earnest who created the program to solve the need of users who wanted information on other users of the network. Information on who is logged-in was useful to check the availability of a person to meet. This was probably the earliest form of presence information for remote network users.