What is the difference between high precision resistors and current sense resistors
Resistors are resistors.  They only see the current thru them and the voltage across them.

However, specific models can be targeted to specific applications.  What you show as a current sense resistor looks like it's designed to dissipate significant power.  However, it would work for lots of purposes within its power and voltage limits.

Current sense resistors tend to:

Be run with little voltage across them.

Be fairly accurate, since being used for measurement.

Drift little due to temperature.

Have low values.

Sometimes have 4 leads so that you can use a Kelvin connection.  Two leads carry the current, then the voltage is measured across the two other leads.  This keeps the voltage drop due to current in the leads off the measurement.