We construct a model in which the least strongly compact cardinal is also the least strong cardinaj isn't supercompact, and for any , if is regular, is strongly compact if and only if is strong.
Arthur W. APTER. "On the level by level equivalence between strong compactness and strongness." J. Math. Soc. Japan 55 (1) 47 - 58, January, 2003. https://doi.org/10.2969/jmsj/1196890841