Is the recorded sales price here the atucal sale price?

Yes. In the tables for any given building on Streeteasy, the sales data are lifted from ACRIS--a government database. Realtor data you get from clicking through to the agency listings (the specific Corcoran or Elliman web page for the apartment), should post accurate sales data, but you can't be certain. ACRIS is the reliable source. If such data is important to you (and it should be in most cases), pay streeteasy the $10/month for "insider" access to the ACRIS information in the tables. It is publicly available, but it is also much easier to see at a glance on Streeteasy without a thousand clicks.

That said, a number of realtors will try to obscure the data and fool the consumer by preventing the recorded sales price from appearing. They do this by taking the listing off the market before the recorded sales price can be uploaded, with the notation "Listing no longer available" or "Recently sold" under the last available listing price. The recorded sales price will not be listed in the left-hand column, and the listing price will be the last price associated with the listing. The purpose of this is to trick people into thinking that the property sold at or near the listing price when it may have actually sold for significantly less than the listing price. Thus, if you cannot trace the price back to ACRIS, then don't trust it.