Laser cavities which can generate different types of ultrashort pulses are attractive for practical applications and the study of pulse dynamics. Here, we report the first experimental observation of both conventional solitons (CS) and dissipative solitons (DS) generated from a single all-fiber laser with net-anomalous dispersion. A birefringence-related intracavity Lyot filter with an adjustable extinction ratio enables the switching between the two types of ultrashort pulses. Depending on the polarization controller settings and the pump power, either chirp-free CS with a pulse energy of 406 pJ and a spectral bandwidth of 5.1 nm or up-chirped DS with a pulse energy of 5.1 nJ and an optical bandwidth of 9.6 nm can be generated. Similar polarization features are observed when the laser switches between different soliton operations as both CS and DS are group-velocity-locked vector solitons. Our work paves a novel way to generate dissipative solitons with a relatively high pulse energy (one order of magnitude larger than for CS) and a large chirp directly from an all-fiber net-anomalous-dispersion cavity through birefringent filter management.