A manned mission to Mars is entirely feasible with current technology. In fact I'd argue it'd have been feasible with 1980s technology, it was simply costly. If we (we as in humankind) wanted, we could have a base on Mars for some time now.
Who is to say what our capabilities will be in 50 years? In 100 years?
A manned mission to another solar system is going to be very-very difficult, we'd need generational space ship/habitats. Note that difficult is not the same as impossible. Such a ship could be feasibly constructed with modern day technology, but it would be enormously costly so there was no motivation to do it.
I'd agree with your point that a mission to another galaxy is basically unimaginable with technology we can realistically theorize about today. We'd need extremely exotic physics which are unlikely to be doable ever.