ReactRouter's strict prop defines if there is a strict entry of requested path in pathname, as described in docs. For example, if you wish not to handle the page's route without trailing slash, your Route can be described like this:
<Route path="/mypath/" strict ... />
So the pathname /mypath won't be handled with this Route, and the pathname /mypath/ will be. Note, that in this mode this Route will also catch other child-routes, e.g. /mypath/childroute, /mypath/childroute/childroute2, etc, but it won't catch route /mypath?query=.... Think about this prop like if you are using "string".includes("substring"):
"/mypath".includes("/mypath/") => false
"/mypath/".includes("/mypath/") => true
"/mypath/kappa".includes("/mypath/") => true
The exact prop is used to define if there is an exactly the requested path.
Usually it is used to wrap routes without child-routes (e.g. homepage).
<Route path="/" exact ... />
<Route path="/" ... />
First route will catch only routes like mydomain.com, mydomain.com/, mydomain.com/?query=... etc. The second will catch all routes, e.g. both of mydomain.com and mydomain.com/myroute.