【Misplace】 , 【mislay】  both mean to put in the wrong place and both in their basic use imply that the thing in question is as unavailable as if lost though firmly believed to be still in one's possession.

【Misplace】 basically implies a putting of a thing in another than its proper or customary location, but it more often suggests a setting or fixing of something where it should not be.

【Mislay】 usually implies a misplacing in the basic sense but stresses a forgetfulness of the place in which the thing has been put; it therefore often means to lose through misplacing.

In its extended use it differs little from lose.