Just bought a 1960 house with unfinished portion of a basement that has had previous water intrusion and the crack has been injected. There are a few lingering cracks I want to deal with. Wall has weird stucco/popcorn type of concrete coating, swirled on about 1/16 inch thick. I want to put liquid rubber primer and a sealant on this entire wall. Can I just primer it then seal it with a liquid rubber product as it is or should I get to bare concrete? Thanks!
Water – Basement Wall with Stucco/Concrete that needs to be removed
basementconcretefoundationstuccowaterproofing
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You are looking for leveling compound for concrete. That link is to one of many of Home Depot's choices for a fast setting mix which can be up to one inch thick. The reviews say the instructions should be carefully followed; many rave about the results. I imagine if you mucked up the application, it could be difficult to correct. (I have only done leveling compound on top of a wood subfloor: that was pretty easy to get right.)
Two common types of things are sprayed on basement walls.
What I suspect you have there is a white "waterblocking" coating - something like UGL Drylock (not an endorsement, just an example. I prefer waterbase version) 
(source: drylok.com)
It can be brushed or rolled, and a vigorous rolling may well provide the spatter you see. It's also becoming common to see sprayed-on polyurethane foam in basements (it's better put on the outside, but if retrofitting, putting it on the inside doesn't involve excavating all around the building) but that's usually a bit thicker and somewhat yellow (plus it's obviously plastic when you touch it.)
Best Answer
That is a skim coat and depending on how well it was applied it can be difficult to remove. I use a needle scaler (welders use these to relieve stress and quickly clean slag from rust) I got my first one from harbor freight years ago and literarily war it out doing similar work. It is not hard but time consuming. I don’t know if there is an electric version but it was recommended by a friend that is a millwright. needle scaler. I googled needle scaler and there are quite a few on line the last one I purchased from HF has probable been used over 100 hours, the one before that lasted 10+ years they really make the job easy. I have no connection to HF except having purchased a few of there tools some are real junk but I have a few that have been recommended by friends that have lasted well beyond my expectations.