The Developmental Mechanics of Cell Specification (https://www.ncbi.nlm.nih.gov/books/NBK9968/)

An embryo's environment may be a tide pool, a pond, or a uterus. As we saw above, the embryo interacts with its environment, and its developmental trajectory can be guided by information from its surroundings. On a smaller scale, the environment of an embryonic cell consists of the surrounding tissues within the embryo, and the fate of that cell (for instance, whether it becomes part of the skin or part of the lens) often depends upon its interactions with other components of its immediate “ecosystem.”

Thus, a second research program of experimental embryology studies how interactions between embryonic cells generate the embryo. The development of specialized cell types is called differentiation (Table 3.2). These overt changes in cellular biochemistry and function are preceded by a process involving the commitment of the cell to a certain fate.At this point, even though the cell or tissue does not appear phenotypically different from its uncommitted state, its developmental fate has become restricted. The process of commitment can be divided into two stages (Harrison 1933; Slack 1991). The first stage is a labile phase called specification. The fate of a cell or a tissue is said to be specified when it is capable of differentiating autonomously when placed in a neutral environment such as a petri dish or test tube. (The environment is neutral with respect to the developmental pathway.) At this stage, the commitment is still capable of being reversed. The second stage of commitment is determination. A cell or tissue is said to be determined when it is capable of differentiating autonomously even when placed into another region of the embryo. If it is able to differentiate according to its original fate even under these circumstances, it is assumed that the commitment is irreversible.*

Autonomous cell fate specification is a form of embryonic specification in which a developing cell is able to differentiate (become a cell carrying out a specialised function) without receiving external signals. 

In Wiki:

Cell fate determination (https://en.wikipedia.org/wiki/Cell_fate_determination)

The determination of a cell to a particular fate can be broken down into two states where the cell can be specified (committed) or determined. In the state of being committed or specified, the cell type is not yet determined and any bias the cell has toward a certain fate can be reversed or transformed to another fate. If a cell is in a determined state, the cell's fate cannot be reversed or transformed. In general, this means that a cell determined to differentiate into a brain cell cannot be transformed into a skin cell. Determination is followed by differentiation, the actual changes in biochemistry, structure, and function that result in specific cell types. Differentiation often involves a change in appearance as well as function.

Modes of specification

There are three general ways a cell can become specified for a particular fate; they are autonomous specification, conditional specification and syncytial specification.