A screw-type container and closure system that has: a container that comprises a first subassembly: the first subassembly comprises: a reservoir that is able to be filled with a product, and that has a threaded neck with screw threads; a container overshell having a closed bottom and an opened top into which is disposed the reservoir; and one or more magnetic elements disposed near the top of the container overshell; a closure that comprises second and third subassemblies: the second subassembly comprises: an overcap having an opened, distal end, and a closed, proximal end; one or more magnetic elements located near the opened, distal end of the overcap; the third subassembly comprises: a screw-threaded inner cap that is housed within the overcap, and that has a top surface and a bottom edge; a wand that depends from an inner surface of the inner cap; and an applicator surface that is supported at the end of the wand; wherein: the screw-threaded inner cap and the overcap are stationary with respect to each other in rotation, but the inner cap is able to slide up and down within the overcap, between a lower position and an upper position; a spring disposed between the inner cap and the overcap, so as to urge the inner cap downward relative to the overcap; and when the screw-threaded inner cap is fully rotated onto the threaded neck, a magnetic attraction between the one or more magnetic elements disposed near the top of the container overshell and the one or more magnetic elements located near the opened, distal end of the overcap is sufficient to overcome the bias of the spring, and urge the overcap downward until it contacts the container overshell. a container that comprises a first subassembly: the first subassembly comprises: a reservoir that is able to be filled with a product, and that has a threaded neck with screw threads; a container overshell having a closed bottom and an opened top into which is disposed the reservoir; and one or more magnetic elements disposed near the top of the container overshell; a reservoir that is able to be filled with a product, and that has a threaded neck with screw threads; a container overshell having a closed bottom and an opened top into which is disposed the reservoir; and one or more magnetic elements disposed near the top of the container overshell; a closure that comprises second and third subassemblies: the second subassembly comprises: an overcap having an opened, distal end, and a closed, proximal end; one or more magnetic elements located near the opened, distal end of the overcap; the third subassembly comprises: a screw-threaded inner cap that is housed within the overcap, and that has a top surface and a bottom edge; a wand that depends from an inner surface of the inner cap; and an applicator surface that is supported at the end of the wand; the second subassembly comprises: an overcap having an opened, distal end, and a closed, proximal end; one or more magnetic elements located near the opened, distal end of the overcap; an overcap having an opened, distal end, and a closed, proximal end; one or more magnetic elements located near the opened, distal end of the overcap; the third subassembly comprises: a screw-threaded inner cap that is housed within the overcap, and that has a top surface and a bottom edge; a wand that depends from an inner surface of the inner cap; and an applicator surface that is supported at the end of the wand; a screw-threaded inner cap that is housed within the overcap, and that has a top surface and a bottom edge; a wand that depends from an inner surface of the inner cap; and an applicator surface that is supported at the end of the wand; wherein: the screw-threaded inner cap and the overcap are stationary with respect to each other in rotation, but the inner cap is able to slide up and down within the overcap, between a lower position and an upper position; a spring disposed between the inner cap and the overcap, so as to urge the inner cap downward relative to the overcap; and when the screw-threaded inner cap is fully rotated onto the threaded neck, a magnetic attraction between the one or more magnetic elements disposed near the top of the container overshell and the one or more magnetic elements located near the opened, distal end of the overcap is sufficient to overcome the bias of the spring, and urge the overcap downward until it contacts the container overshell. the screw-threaded inner cap and the overcap are stationary with respect to each other in rotation, but the inner cap is able to slide up and down within the overcap, between a lower position and an upper position; a spring disposed between the inner cap and the overcap, so as to urge the inner cap downward relative to the overcap; and when the screw-threaded inner cap is fully rotated onto the threaded neck, a magnetic attraction between the one or more magnetic elements disposed near the top of the container overshell and the one or more magnetic elements located near the opened, distal end of the overcap is sufficient to overcome the bias of the spring, and urge the overcap downward until it contacts the container overshell.