In ASK, a carrier is multiplied by a set of discrete amplitudes, depending on the information bits. In practice, binary ASP (BASK) is often used, where one of the amplitudes is zero, i.e. for a digital \$0\$, the modulated signal is zero, and for a digital \$1\$ the modulated signal is the carrier multiplied with some fixed amplitude. This important special case of ASK is called on-off keying (OOK).
Digital PAM is a digital modulation format where a pulse is multiplied by the current data symbol. In this sense, ASK can be seen as a special case of digital PAM, where the pulse is a sinusoid with the carrier frequency over one symbol interval. In general, the digital PAM signal can be written as
where \$A_k\$ are the discrete symbols, \$p(t)\$ is the pulse function, and \$T\$ is the symbol interval. Note that \$A_k\$ can be any set of discrete symbols. Usually the number of symbols is a power of \$2\$. E.g., if the number of symbols is \$2^m\$, each symbol carries \$m\$ bits. Note that the signal \$s(t)\$ in (1) can be modulated by a carrier. In the general case, the symbols \$A_k\$ can be complex-valued, and a passband signal is generated by
where \$\omega_c\$ is the carrier frequency in radians. Equations (1) and (2) are the general representation of digital passband PAM. Quadrature amplitude modulation (QAM) and phase shift keying (PSK) are special cases.
Note that the type of PAM explained in nidhin's answer is analog PAM.