For the purposes of high school physics it is reasonable to say that electric fields start and stop on charges but magnetic fields always run in loops.

This fails to be rigorous in at least two ways:

• Relative velocity mixes the two types of fields in a manner governed by the Lorentz transform, so the truth is like wsc says.
• It is an open question if there exist any magnetic monopoles, but theoretical prejudice favors their existence for reasons of beauty.

For the purposes of high school physics it is reasonable to say that electric fields start and stop on charges but magnetic fields always run in loops.

This fails to be rigorous in at least two ways:

• Relative velocity mixes the two types of fields in a manner governed by the Lorentz transform, so the truth is like wsc says.
• It is an open question if there exist any magnetic monopoles, but theoretical prejudice favors their existence for reasons of beauty.