Many things to cover...
The 38 S&W is an old black powder loading.
The .38 Special is an older smokeless powder loading.
One is short, one is long, one is fat, one is not, one was the standard for police for years and years.
A Model 15 Smith and Wesson revolver is a great classic. I have never seen one that was not a .38 Special (have seen some Model 14s and 10s in .38 S&W). The "Special" uses a bullet from .355 to .360 with the target diameter of .357 for jacketed bullets and .358 for lead. The smaller bullets may not seal off and would lead the barrel excessively. The larger diameter bullets will generate greater pressures and will lead the barrel excessively. This is for lead bullets. Jacked are another ball park.
The .38 S&W is a great old pea shooter. The actual bore diameters vary greatly. The standard bullet diameter is .360 for lead.
Yes you could load .360 bullets into a .38 Special. I see a number of potential problem. First, you are learning to load lead and loading over sized bullets would not be a beginner's project. The bullets may well bulge your .38 Special cases to the point that they will not chamber. Expect a lot of leading and the loads would have to be reduced because of the swaging down process. I would advise against using those bullets and more so as a beginning/learning bullet.
Next up, bullet types. All bullets are bullets. But they don't all load equally. Lead is slick, jacketing is hard, plated bullets are someplace in between. Get several loading data sources (books/manuals/powder company information/bullet company information - paper and or on-line), read them. Use the 'Starting' load specs to 'start' for the components you are using and work up till you get the results you are satisfied with. The 'Starting' load specs will be different between lead and jacketed and plated. With lead, lighter weight bullets may be substituted if the spread isn't too great. Jacked bullets have more variables to deal with. Length of bearing surface, hardness of the core lead, stiffness of the jacket material all may have great impact upon the 'safe' loading point. Remember, the listed "MAXIMUM' loading is not a challenge.
I used multiple loading sources and compare them to each other before ever loading. Tpyos happen all the time.
If you get bogged down, PMessage me. I'm in the south part of Cass County.
Please load with safety and enjoy,