Is there any difference between the two, like there is between .223 and 5.56? (charge wise for example)
I'm thinking about an AR-10 someday down the road...

Yes, there is a difference between a .308 and 7.62x51 as well as a .223 and 5.56x45.

The .223 and the .308 are what most people to believe are "hunting" loads, so the chamber tolerances need to be tighter for better accuracy.  These loads confirm to the SAAMI specifications.

The 7.62 and 5.56 are military loads where the chambers are not as tight, but will relaibly work under combat conditions.

Dimensionally there is a very slight difference between the pairing rounds, but sometimes a .002 of an inch is enough to make a difference

I have also heard that .308 is loaded (or can be loaded) to higher pressures per SAAMI specifications than 7.62x51 is.  I think I saw that on the DSArms webpage or maybe FAL Files.

yes there is a difference the .223 is loaded to SAMMI spec's and is in Inch dimensions, the 5.56 ammo uses crimped cases thicker case and is in metric dimension's plus the pressure's are higher using Ball powder. it is said you can use .223 in a 5.56 but you cannot should not use 5.56 in a .223 chamber. I used to reload.

I should probably reword my question:

I'm very well aware of the differences between .223 and 5.56.
What I was asking was if the same rule applies for .308 and 7.62

But thanks for the replies so far, and I found what I was looking for.

Yes...308 is loaded to a higher pressure.  That is why it is not recommended to shoot .308 in surplus 7.62x51 guns i.e. FR-8.