Here are the words sorted into 4 groups of 4:
Group 1: Related to 'food' or 'eating'
- Cater
- Bowl
- Hash
- Bed (as in "bed & breakfast")
Group 2: Related to 'actions'
- Throw
- Touch
- Shred
- Plan
Group 3: Related to 'star/astronomy'
- Star
- Caret (used in math/physics contexts, but it's also a symbol that can resemble a zig-zag in starlike graphics)
- Trace
- Host (as in hosting an event, which can be star-related)
Group 4: Related to 'constructing/shaping'
- Caret (used in writing/editing)
- Crate
- Brace
- Collar
This classification mixes both meanings and possible interpretations of the words. Alternatively, they could be categorized in ways that relate to even broader or different themes depending on context.