In the US, licences at each level (private, commercial & airline transport) are segregated by category (fixed wing, rotary wing, balloon etc) & class. In the fixed wing category the classes are Single Engine Land, Single Engine Sea, Multi Engine Land & Multi Engine Sea (SEL, SES, MEL & MES, respectively).
Having gained a licence at any particular level, on a category/class eg a Private licence on a MEL, then you're licenced to fly *any* MEL that doesn't specifically require training or a type rating. An MU2 is a type that requires training. All jets require type ratings but not generally turboprops or piston aircraft <12,500lb take off weight). So, do your Private in a BE76 Duchess, and you're legal to go fly a Kingair 200 - as long as you're familiar with its handling & the normal & emergency procedures.