Yep. The Czech verbs of motion have two different forms 'determinate' and 'indeterminate,' similar to 'imperfective' vs 'perfective.'

jít 'walk, go on foot' (determinate) conveys the meaning of 'single, one-directional, goal-directed action.'

vs.

chodit 'walk, go on foot' (indeterminate) conveys the meaning of 'repeated, habitual, multi-directional and general (non-goal-directed) activity.'

The same applies to jet vs jezdit, běžet vs běhat, lětet vs létat and several others.

(from James Naughton's Czech: An Essential Grammar.)

"Domů" is not a noun, but an adverb meaning 'to home' and thus not declined.

'At home' is "doma."