Any difference between "protest" and "protest against"?

I've looked up in my Oxford Advanced Learner's Dictionary and New Oxford American Dictionary, it turns out that the difference (if any) between "protest sth" and "protest against sth" looks very hard to tell. Examples are as follows:

1. Students took to the streets to protest against the decision.
2. They fully intend to protest the decision.
3. Doctors and patients protested against plans to cut services at the hospital.
4. The workers were protesting economic measures enacted a week earlier.

In addition, I'm wondering if the object following them really matters to the choice, but examples 1 & 2 seem to prove me wrong. Any more explanation on this?

Your examples 1 and 3 use protest against and 2 and 4 just use protest without against.

British English uses against; American English does not (and BrE seems to be following suit).

protest verb
1 [no object]
express an objection to what someone has said or done:
before Muriel could protest, he had filled both glasses
• publicly demonstrate strong objection to an official policy or course of action:
   doctors and patients protested against plans to cut services at the hospital
   [with object]: North American
   the workers were protesting economic measures enacted a week earlier

[ODO]