If it has a closed toe, it's not a sandal.
If it's got a strap for the toes and no other strap... it's a jandal. This is particularly true if it's a thong type strap.
If it's otherwise open toed, it's a sandal.
If it has a closed toe and no holes revealing the foot (or sock) within, it's a shoe or a boot. Boots are probably defined by whether or not the "shoe" goes over the ankle.
If it has a closed toe and is of a flexible fabric with a reinforced sole, it's a shock. Basically only babies and very young toddlers wear these.
If it's otherwise close toed, it's a shandal.
Socks in jandals and sandals... looks unusual, unless the wearer looks like an adult man and is wearing sandals. No socks in shoes... look odd. No socks in shandals... honestly, looks odd. There's nothing wrong with these... although socks are immensely practical when it comes to wearing shoes... it's just that too few people do these things for them to not look unusual. (Adult men rarely wear, in my experience, sandals without socks so the norm reference differs.)
The only people who should give a shit about shoe brands are people cannot reliably find shoes in their size. This means anyone who wears bigger than UK 12/US 13/EU 47 because a metric crap tonne of companies literally do not manufacture shoes in such sizes. Hence, paying attention to brands is a practical matter.
Bare feet are obviously the superior "footwear" unless the ground is dangerous or extremely muddy. In the latter case, I suggest gumboots.
Because, you know. Sufficient mud will rip your shoes right off... not good if it's an oyster bed you're walking on (trust me on this).
EDIT: dammit, forgot that slippers were a thing... if they're not shocks and intended to be worn inside (as in pretty much exclusively) then whatever they look like, they're slippers.
I think that's covered all bases.