Thank
you for these four items, Sam. They are clearly all from the same
lexical field. What you need to know is what restrictions are placed
on their use.
Equipment
usually describes (all) the necessary articles for a purpose. Thus
you would say:
'A lot of equipment was needed for this mountaineering
(or camping) expedition.'
Apparatus is similar in meaning to equipment, although
it tends to relate to particular contexts. Thus gymnastic apparatus
refers to all the apparatus you would expect to find in a gym. It
tends to be used in scientific or technical contexts:
'The chemistry lab was full of the apparatus needed for a range of
experiments'.
For
tools and utensils it is also very important to know
which other words they collocate with. For example, we talk about
garden tools for a gardener and work tools for a carpenter,
but kitchen utensils for a housewife or house-husband.