Everyone has good answers here, but I'd like to point out that a demonstration always seems to be something organized, while a protest seems to be done without much planning. In both cases, people will gather together to chant, wave signs, and stand together, but demonstrations seem to have much more thought go in to them, such as organizing a date and time to be at a certain place, people speaking to a crowd with prepared things to say, etc. Protests may loosely have some things planned, but they seem a bit more chaotic because there isn't much direction or specific people leading what they're doing. All in all, they are similar in a sense of gathering ordinary citizens together in a group to bring awareness to a situation. With my description and the added thoughts from others, we have absolutely seen both demonstrations and protests lately. Organized groups and impromptu protests. Some very peaceful, and some erupting into aggression. Both have the same intent to bring awareness to a situation that they want changed.

A demonstration is not necessarily a protest. If people march through the streets with slogans "We love the current government", it would be a demonstration but not a protest.

They're synonyms, but protest is more specific. Protests denote an objection, while a demonstration is an act of demonstrating. While it is possible to engage in an act of demonstrating something unrelated to an objection, in English native-speak, they are used synonymously (same thing).

The Oxford Advanced Learners Dictionary defines a demonstration as “a public meeting or a march (= an organized walk by many people) at which people show that they are protesting against or supporting somebody/something.” Merriam-Webster’s Learner’s Dictionary defines a protest as “an event at which people gather together to show strong disapproval about something.” Basically, the distinction is that a protest is a display of opposition or disapproval, while demonstrations can be either in opposition to or in support of something or someone. In the recent case of George Floyd’s murder, a Google search has over 3 million hits for “George Floyd protest,” the more appropriate term, and fewer than 200 thousand for “George Floyd demonstration.”

There is very little difference. Those sentences could easily refer to the same event. The words "demonstration" and "protest" are identical in this context. Demonstration has another meaning. It can mean showing someone how something is done. "The teacher gave the student a demonstration". But, in this case, the meaning is obviously "protest". I looked at the definition for "demonstration" in a few dictionaries, and most of them include the word "protest"! The only other difference is tone. I think "demonstration" is a little more positive.