There are many problems with this comparison. Just from the top of my head, the picture is flawed for these reasons:

• The pictured compared two very different time-frames, the "Muslim" Conquest extended from 632 to the Ottoman conquests of the 17th Century, whilst the Crusades picture only covered the famous crusades to the Holy Land, not the Fourth Crusade (which conquered Constantinople and other Christian territories), the Reconquista in Spain, and the Baltic Crusades. Not exactly a fair comparison is it?
• What is the definition of a battle? We have no idea about where most of the early battles of the Arab Conquests took place, let alone their size, so the creator of this image definitely just put some random dots in likely places. Visigothic Spain for instance fell in the eighth century seemingly after just one major battle - all those battles in Spain on that map must therefore be the result of later conflicts, which cannot be just characterised as battles between Christians and Muslims, since Al-Andalus was known for its tolerance and internal divisions (though of course this is a generalisation as well).
• Likewise for Crusades map - there were way more than 13 battles, both Tunisia and Egypt were for instance attacked by Louis IX of France. There must have also been many many raids led by crusaders - if we are counting Muslim raids into France, why not the crusaders'?
• The causes of battles between Muslims and Christians were complex. The armies during the rise of Islam for instance definitely included Arab Christians and Jews in their ranks, whilst many Muslims allied with Christian powers during the later Crusades as well. Muslims and Christians did co-exist and we should never see the past as being entirely made up of conflicts or peace - it was mostly a mixture of both.

This comparison is blatantly made to make a political point, not to represent the historical reality. A look through any modern scholarship on the Arab Conquests would for instance reveal that the Conquests, as far as conquests go, were fairly mild. Sieges and massacres were rare and toleration was the norm rather than pogroms or expulsions. I know a lot less about the Crusades, but I know enough to say that they were very complex as well - reducing history to misleading pictures like this is very dangerous and ought to be refuted at every possible opportunity.

what does it ACTUALLY show?

It shows that some people have an addiction to abusing history to make political points.

Seemingly every battle fought by any medieval or early modern Muslim army is listed as "Muslim Conquest Battles", whilst only a few Crusader battles are listed as "Crusade Battles" (note how it very conveniently leaves out the battles the Fourth Crusade fought against the very Christian cities of Zara and Constantinople, the Albigensian Crusade fought against "heretics" in Southern France, and the entire Northern Crusade in the Baltic region).

However, it is ludicrous to say that every battle fought by every Muslim army was motivated solely by Islam. If we are going to call all battles fought by Islamic armies against non-Muslim armies "Muslim Conquest Battles", then why not apply that same standard to battles fought by Christian armies against non-Christian ones? If we do so, we'd end up with a map of "Christian Conquest Battles" that would feature dots over every continent except Antarctica. The Aztecs that Cortes fought certainly weren't Christians.

Of course, it is ludicrous to label all of European colonialism and imperialism as being "Christian Conquest Battles", because, as many know, the motivations behind colonialism and imperialism were more complex than religion alone. However, it is very common for people to accept that European leaders have complex motivations beyond religious zeal - things like a desire for land, resources, political influence, security, et cetera - whilst attributing every war fought by Islamic powers against non-Muslims as being simply motivated by the desire to spread Islam.

That being said i've been watching the dynamic map on mute and i think there is an interesting implicit moral claim regarding say Spain here: the 200 battles include seemingly all inter religious wars and battles not differentiating who initiated the battles and why. 1. lots of the pre 1090s battles were Christian states advancing before the almoravid invasions and 2. they aren't really very religious wars. But if Islam invaded Spain it remains a religious outsider invading until it is forced out.

I would argue modern eyes often take a similarly ahistoric approach to latter crusader states: viewing them as illegitimate states on Islamic land instead of long existing parts of the landscape. If he considered the reconquista a crusade it would be interesting to see how he would map the spanish dots for instance (but that would be an error in classification).

factually i would argue all Warner has really done is collect 550 examples of inter religious conflict between Christians and Muslims on a map. That can be useful it just doesn't really prove his point considering 1. 500 battles in 1200 years. 2. Carries an implict claim that these are all the same type of religious conflicts (which is wrong) 3. as mentioned below, he doesn't attempt an apples to apples comparison.

Thanks everyone for the responses and well-thought out insight! I appreciate it.