In order to study the Gamow-Teller (GT) transitions from the T-z = +2 nucleus Ca-44 to the T-z = +1 nucleus Sc-44, where T-z is the z component of isospin T, we performed the (p, n)-type (He-3, t) charge-exchange (CE) reaction at 140 MeV/nucleon and the scattering angles 0 degrees and 2.5 degrees. An energy resolution of 28 keV, that was realized by applying matching techniques to the magnetic spectrometer system, allowed the study of fragmented states. The GT transition strengths, B(GT), were derived up to the excitation energy (E-x) of 13.7 MeV assuming the proportionality between cross sections and B(GT) values. The total sum of B(GT) values in discrete states was 3.7, which was 31% of the sum-rule-limit value of 12. Shell model calculations using the GXPF1J interaction could reproduce the gross features of the experimental B(GT) distribution, but not the fragmentation of the strength. By introducing the concepts of isospin, properties of isospin analogous transitions and states were investigated. (i) Assuming isospin symmetry, the T-z = +2 -> +1 and T-z = -2 -> -1 mirror GT transitions should have the same properties, where the latter can be studied in the beta decay of Cr-44 to V-44. First, we confirmed that the beta-decay half-life T-1/2 of Cr-44 can be reproduced using the B(GT) distribution from the Ca-44(He-3, t) measurement. Then, the 0 degrees, (3He, t) spectrum was modified to deduce the "beta-decay spectrum" and it was compared with the delayed-proton spectrum from the Cr-44 beta decay. The two spectra were mostly in agreement for the GT excitations, but suppression of the proton decay was found for the T = 2 isobaric analog state (IAS). (ii) Starting from the T = 2 ground state of 44Ca, the (3He, t) can excite GT states (state populated by GT transitions) with T = 1, 2, and 3. On the other hand, the Ca-44(p, p') reaction can excite spin-M1 states (states populated by spin-M1 transitions) with T = 2 and 3 that are analogous to the T = 2 and 3 GT states, respectively. By comparing the spectra from these two reactions, a T value of 2 is suggested for several GT states in the E-x = 11.5-13.7 MeV region. (iii) It has been suggested that the T = 2, J(pi) = 0(+) double isobaric analog state (DIAS) at 9.338 MeV in the T-z = 0 nucleus Ti-44 forms an isospin-mixed doublet with a subsidiary 0(+) state at 9.298 MeV. Since no corresponding state was found in the T-z = +1 nucleus Sc-44, we suggest T = 0 for the subsidiary state.