MANET is pretty well defined as an Internet Protocol scheme. A MANET is built at layer 3, in short. You can go to the IETF site and find multiple RFCs written about MANET, including a version of OSPF routing protocol for MANET, and other routing protocols such as DSDV, OADV, and DSR developed for MANET. Layer 3 schemes, all of them. They work with IP addresses.
Wireless ad-hoc networking is a more generic term. It can apply to layer 2 schemes, such as the use of IEEE 802.11 (WiFi) in so-called "ad hoc" mode, as opposed to the more typical use of WiFi in "infrastructure " mode. For example, for vehicular ad-hoc networks, or VANET, I don't think it's clear that a layer 3 MANET scheme is the future. And there are any number of wireless ad-hoc network concepts out there - such as wireless sensor networks (WSNs) often mentioned in IoT discussions. Any type of self-organizing wireless system, not dependent on a base station or other single infrastructure device, would be considered wireless ad-hoc. I'd say that MANET is a subset, because it is specifically an IP-based concept.
1. Mobile Ad hoc Network (MANET) : MANET consists of number of mobile devices that are connected together to form a network, without any support from an existing internet infrastructure or any other fixed network station. It is autonomous system of nodes connected by wireless links. In MANET the network topology may change dynamically in an unpredictable manner since there is no fixed infrastructure and the nodes are free to move, but each node have limited transmitting power. MANET’s are basically peer-to-peer, multi-hop wireless network in which packets are transmitted in store.
2. Vehicular Ad Hoc Networks (VANET) : VANET is similar to MANET in terms, that is also do not need any infrastructure for data transmission. VANET play important role in aspect of safe driving, intelligent navigation, emergency and entertainment applications .It can be defined as an intelligent component of transport system as vehicle are able to communicate with each other as well as roadside base station, which are located at critical points of the road. Example :-Intersection and Construction Sites.