Both are semi-autos and are the same basic gun. Beretta hasn't made a pump gun in years. I don't know what the specific differences are between the two designations but they are not significant. Beretta 390 field guns usually have a more angular receiver while the target guns are rounded.
In any event, Beretta discontinued the 390 and replaced it with the 391 which Beretta claims has an improved gas system.
