One is an "Atmospheric" vessel or tank - which is open by some means (no top or an open vent or other) to the atmosphere.
The other is a "Pressure" vessel - This is a closed container which can have various forms, functions and may or may not have internals.
Examples of "Pressure" vessels are:
Closed "Tanks" for the storage of hydrocarbons such as gasoline(petrol) etc.
Horizontal "Accumulators" which may or may not have a "Boot" and will act as a separator for the removal of impurities.
"Fractionation" Towers - which have trays to strip and separate primary and secondary products from the main stream.
"Reactors" which have some form of "Catalyst" inside which causes a change to the product stream with-out becoming a part of that product. This is normally a continuous process reactor. This "Reactor will normally have a large "Manhole" at the top of the vessel to load the catalyst and another manhole or nozzle at the bottom to remove the catalyst.
"Reactors" which are used as a mix chamber where multiple ingredients are added and then mixed (heated or cooled) to form a finished product. This is normally a batch mode reactor. This type of "Reactor" may be fitted with: mixers, internal cleaning systems (CIP) , internal or external heating/cooling coils or other special features.
All five of these are considered a "Pressure" Vessel
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