ESTs = Expressed Sequence Tags , they date back from when we were doing Sanger sequencing on cloned cDNAs . I would assume this term is not used anymore for 'transcript sequencing' nowadays. They are (were) used in gene prediction as prove of expression of a given region in the genome, hence point to gene locations.
Not sure what you mean with difference between de-novo and ab-initio. Ab-initio usually points to gene prediction approaches that do not use any external evidence (such as ESTs, transcripts, proteins, ... ) they work solely based on properties that can be derived from the genomic sequence itself. The counterpart is called similarity or homology based prediction: those methods use protein, EST, ... information to locate potential gene locations in the genome. With 'de-novo' you perhaps mean that NGS reads are first being (de-novo) assembled into transcripts before they are used in gene prediction (=beneficial because they more resemble complete genes/transcripts)