What are the differences between struct and class in C++?

You forget the tricky 2nd difference between classes and structs.

Quoth the standard (§11.2.2 in C++98 through C++11):

In absence of an access-specifier for a base class, public is assumed when the derived class is declared struct and private is assumed when the class is declared class.

And just for completeness' sake, the more widely known difference between class and struct is defined in (11.2):

Member of a class defined with the keyword class are private by default. Members of a class defined with the keywords struct or union are public by default.

Additional difference: the keyword class can be used to declare template parameters, while the struct keyword cannot be so used.

It's worth remembering C++'s origins in, and compatibility with, C.

C has structs, it has no concept of encapsulation, so everything is public.

Being public by default is generally considered a bad idea when taking an object-oriented approach, so in making a form of C that is natively conducive to OOP (you can do OO in C, but it won't help you) which was the idea in C++ (originally "C With Classes"), it makes sense to make members private by default.

On the other hand, if Stroustrup had changed the semantics of struct so that its members were private by default, it would have broken compatibility (it is no longer as often true as the standards diverged, but all valid C programs were also valid C++ programs, which had a big effect on giving C++ a foothold).

So a new keyword, class was introduced to be exactly like a struct, but private by default.

If C++ had come from scratch, with no history, then it would probably have only one such keyword. It also probably wouldn't have made the impact it made.

In general, people will tend to use struct when they are doing something like how structs are used in C; public members, no constructor (as long as it isn't in a union, you can have constructors in structs, just like with classes, but people tend not to), no virtual methods, etc. Since languages are as much to communicate with people reading the code as to instruct machines (or else we'd stick with assembly and raw VM opcodes) it's a good idea to stick with that.

Quoting The C++ FAQ,

[7.8] What's the difference between the keywords struct and class?

The members and base classes of a struct are public by default, while in class, they default to private. Note: you should make your base classes explicitly public, private, or protected, rather than relying on the defaults.

Struct and class are otherwise functionally equivalent.

OK, enough of that squeaky clean techno talk. Emotionally, most developers make a strong distinction between a class and a struct. A struct simply feels like an open pile of bits with very little in the way of encapsulation or functionality. A class feels like a living and responsible member of society with intelligent services, a strong encapsulation barrier, and a well defined interface. Since that's the connotation most people already have, you should probably use the struct keyword if you have a class that has very few methods and has public data (such things do exist in well designed systems!), but otherwise you should probably use the class keyword.