Precise extraction of ionospheric total electron content (TEC) observations with high precision is the precondition for establishing high-precision ionospheric TEC models. Nowadays, there are several ways to extract TEC observations, e.g., raw-code method (Raw-C), phase-leveled code method (PL-C), and undifferenced and uncombined precise point positioning method (UD-PPP); however, their accuracy is affected by multipath and noise. Considering the limitations of the three traditional methods, we try directly to use the phase observation based on zero-difference integer ambiguity to extract ionospheric observations, namely, PPP-Fixed method. The main goal of this work is to: 1) deduce the expression of ionospheric observables of these four extraction methods in a mathematical formula, especially the satellite and receiver hardware delays; 2) investigate the performance and precision of ionospheric observables extracted from different algorithms using two validation methods, i.e., the co-location experiment by calculating the single difference for each satellite, and the single-frequency PPP (SF-PPP) test by two co-location stations; and 3) use the short arc experiment to demonstrate the advantages of the PPP-Fixed method. The results show that single-difference mean errors of TEC extracted by PL-C, UD-PPP, and PPP-Fixed are 1.81, 0.59, and 0.15 TEC unit (TECU), respectively, and their corresponding maximum single-difference values are 5.12, 1.68, and 0.43 TECU, respectively. Compared with PL-C, the precision of the TEC observations extracted by the PPP-Fixed method is improved by 91.7%, while it is 67.3% for UD-PPP. The SF-PPP experiment shows that PPP-Fixed is the best among these methods in terms of convergence speed, correction accuracy, and reliability of positioning performance. Moreover, the PPP-Fixed method can achieve high accuracy even when the observed arc is short, e.g., within 40 min.