The difference between like/ilike and =like/=ilike is that with like/ilike, Odoo automatically appends and prepends a '%' to the search string before passing it to the database. So [('name', 'like', 'dog')] is equivalent to [('name', '=like', '%dog%')]. So you could use =like if you need to find the search string at the only beginning of the column, for instance [('name', '=like', 'dog%')]

'=?' operator makes the term TRUE if right statement is None or False otherwise behaves like '='

Reference:

openerp/osv/expression.py:1169

if right is False or right is None: 

# '=?' is a short-circuit that makes the term TRUE if right is None or False 

query = 'TRUE'

params = [] 

else: 

# '=?' behaves like '=' in other cases 

query, params = self.__leaf_to_sql( create_substitution_leaf(eleaf, (left, '=', right), model))

Sample: openerp/addons/base/tests/test_expression.py:120

user_ids = users_obj.search(cr, uid, [('name', 'like', 'test'), ('parent_id', '=?', False)]) 

self.assertEqual(set(user_ids), set([a, b1, b2]), '(x =? False) failed')

As it is shown in example, parent_id cannot be False if value doesn't exist: '=?' returns True or parent_id value

ILIKE keyword in PostgreSQL provides case insensitive search.

Reference:-  http://solaimurugan.blogspot.in/2010/07/ilike-operator-in-postgresql.html

Normal odoo 'like' (and 'ilike' for the case insensitive version) allows the use of '%' and '_' within the search parameter.  It uses the SQL 'like' under the hood, which requires '%'s to either side to create the 'contains' operator, as other answers have mentioned.

So '=like' simply does not add those '%'s to either side when converting the operator to SQL.

An easy use case is the "Starts with" search:  ['field', '=like', 'Warren%'].

And the 'Ends with' search: ['field', '=like', '%hat']

And of course the exact search for a phrase with a beginning and an end: ['field', '=ilike', 'My % bag.']

Presumably early Odoo didn't think about the 'Starts With' and 'Ends With' cases.  So 'like', while being very close to its SQL counterpart, was changed in that interpretation of 'like' as 'contains'.  Probably soon afterwards, it was easy enough to remove the 'contains' functionality by adding = to the operator.  This was probably to evoke 'exactly like'  vibes.  If they wanted to evoke a more regex vibe, they should have used '^like$', which makes use of the two anchors from POSIX/Perl(PCRE) regex syntax.  Its ironic that Odoo is built on top of a Postgres DB which supports the 'similar to' operator which is *Very* 'regex like'.