The word "jihad" is like the word "striving" or "struggle" in English. It can be applied to many kinds of struggles, from struggling with one's inner self to armed struggle. Literally, the Arabic word could be used where I used the English word "struggle".

Certain forms of struggle (jihad) have been highlighted by the Islamic tradition and these are most commonly what is meant. Armed struggle is indeed one of them.

However, the Prophet Muhammad (peace be upon him) is reported to have said that this form of jihad was "the lesser jihad". He said that "the greater jihad" (i.e., the greater struggle) is to purify one's own soul.

I highlighted this verse because it presents a third form of struggle that has been particularly emphasized. This is "jihad with the Quran", which as you noted is evangelical in that it involves bringing and embodying the message of the Quran.

I wanted to highlight it because most people (including a number of Muslims, sadly) think that the "great jihad" against those who reject the truth is armed jihad. This is incorrect! The Quran very clearly says that the "great jihad" is to preach and practice the truth.

I should also note that a "rejector" is not the same as a non-Muslim. Many people are non-Muslims but only a few people have knowingly and deliberately chosen to reject Islam. The "great jihad" here is directed at the rejectors, not at non-Muslims in general.

What all of this means is that when there are people who are actively and deliberately rejecting Islam as a religion, then Muslims should convey the truth of the Quran to them. Not attack or kill them.

There are very detailed rules in Islamic law about when armed struggle (what is commonly meant by "jihad") is authorized. These are very similar to the rules that Christians have developed in "just war theory".

One of the later verses in this series will provide further information about this.

Islam is a complex, inter-related whole and it would be distorting to take any part of it out of context with the rest.