The first (car-part.com) is essentially a way for you to find out what the wrecking yards have listed on their online inventory. Remember that each wrecking yard has their own quirks and some are great to work with and others will bend you over and over and over. Case in point, I never go to the local wrecking yard anymore, but will travel 100 miles to one that has a much better return policy and generally better pricing too.
The second (
www.pullapart.com) would be for a wrecking yard chain that as you noted, you pull your own engine. Depending on how long the donor car has been in the lot, there might be some parts pulled from the engine mostly alternators and the like. The advantage would be you can inspect the engine youself before pulling it and be able to get an idea if it is any good before buying it.
Before you pull an engine, you will want to drop the oil pan and look for signs of problems like metal shavings or white gunky oil, You can also pull a valve cover off and check the top for unusual wear. Pull the spark plugs out, put a little oil in the spark plug holes and see if you can turn the engine over from the nut on the harmonic balancer.
Remember cars that are in these yards that have no major body damage are usally there for either bad engines or bad transmissions. Also keep in mind that cars with major body damage can also have an adverse effect on the mechanical soundness of the engine.
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90 Lexus ES250 Auto, 90 Lexus ES250 Stick, 88 Camry LE AllTrac Stick, 88 Camry Wagon

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