It is best to have some authoritative references on hand for factual information about these things,rather than just repeating various internet musings,which are most often wrong.
For the 1903 Springfield and derivatives there are excellent books by Brophy,Campbell,Canfield and Ferris. For the M1 Garand see books by Canfield and Scott Duff. Poyer has books on both rifles which are useful,but contain errors.
M1903A3/A4 rifles were produced by Remington with both 2 and 4 groove barrels depending on production dates. Smith Corona 03A3 rifles were fitted with 4 or 6 groove barrels,again depending on production dates. There is some debate about whether or not Smith-Corona used 2 groove barrels in production. Remington produced large quantities of 03A3 replacement barrels with 2 groove rifling. M1 Garand rifles were not produced with 2 groove barrels,nor were 2 groove barrels provided as GI spares. If you have a 2 groove Garand barrel,it will be one of the "humped up" commercial offerings.