Select record using comma separated string in Like operator in SQL Server

hello,

i have column in sql where i stored comma seperated values like

'cat, lion, donkey,'

in the sql query i want to search any one of the result show the data for e.g

select * from animal where type like '%'+ "cat, tiger," +'%" it should return above row and where ever it find cat or tiger in comma seperated column

but if search parameter are

select * from animal where type like '%'+ "zebra, dinosour," +'%"so in my example i do not have zebra or dinosour any where so it should not return any row

please advice how to acheive it