"Puppet" is the general term although
"marionette" is preferred when referring to a wooden puppet. A cloth puppet with an opening for the hand is often called a "glove puppet"
refs:
Puppet: "figure of a person or animal usually with a cloth body and hollow head that fits over the hand" (Merriam Webster online dict.)
"small figure moved especially by strings as entertainment" (Oxford online dictionaries)

Marionette: "usually wooden figure (as of a person) with jointed limbs that is moved from above by manipulation of the attached strings or wires" (Merriam Webster online dict.)