The influence of the different terminal groups (hydroxyl, methyl) on the properties and phase behavior of PEO in aqueous solutions has been studied analytically. We have generalized our previous model to account for the competition for proton donors and acceptors among four types of hydrogen bonding (donors are mentioned first): water-PEO, water-water, PEO-water, and PEO-PEO. We found that for PEO terminated at both ends by methyl groups the influence of the end groups is minor, similar to infinitely long PEO. Termination of PEO by hydroxyl groups results in hydration enhancement in the poor hydration regions, i.e., at high polymer concentration (low water content) and at high temperature. The contribution of end groups to overall hydration is especially strong for short polymer chains and decreases with chain length as 1/N, but it remains larger than 1% for chains with N less than or similar to 250 (for equal fraction of polymer and solvent, Phi = 0.5) or with N less than or similar to 460 (for Phi = 0.9). For a polymer volume fraction less than about 0.886, the contribution of end group to hydration increases with temperature and for polymer solutions of higher concentration it decreases with temperature (due to competition with PEO-PEO hydrogen bonding). We also discuss the possibility of physical cross-linking of PEO either via direct PEO-PEO hydrogen bonds or via a single water molecule acting as a cross-linking agent. We found that the degree of cross-linking considerably increases with chain length and also is strongly enhanced for hydroxyl-terminated short chains. Hydration via end groups also results in a chain length dependence of the second virial coefficient, A(2). For one- or two-end hydroxyl-terminated PEO, the second virial coefficient decreases with a chain length increase whereas for the methyl-terminated PEO A(2) increases with an increase in chain length, tending to the same constant limit for infinitely long chains. The phase diagram calculated accounting for hydration via terminal hydroxyl groups features considerably improved agreement between theoretical predictions and experimental observations for short PEO chains: theoretical curves become more centered around experimental data and the chain lengths used for calculations are close to the molecular weight of experimental samples. Theoretical predictions become more consistent for the whole range of chain lengths studied. As a result the lower (LOST) and upper critical solution temperatures (UCST) for hydroxyl-terminated PEO agree very well with different experimental data. Comparing the critical points (UCST and LOST) for polymer chains terminated by different end groups we found that while all curves merge in the long chain limit (N > 300 for LCST and N > 500 for UCST), for shorter chain lengths curves deviate from each other considerably, reaching double critical points (where the UCST merges with the LCST) at different N. Termination of PEO by one hydroxyl group improves the solubility of PEO chains to an extent that it is equivalent to decreasing of chain length by 10 monomer units and adding a second hydroxyl group doubles the effect.