Both of them are verbs. 定 has the meaning of "decide". 订 has the meaning of "book" . normally, they can be exchanged with each other, but in the situation get relation with law, they have a big difference. 定， means the conditions are confirmed already, they can not be revised any more. It emphasize result. For example, 定金，定购。 订， means the conditions are just a agreement, they may be revised. It emphasize the PROCESS. For example. 订婚，订货。 定价，can not be 订价。

sign a contract or document：签订合约/文件

● 定 dìng ◎ 不动的，不变的：～额。～价。～律。～论。～期。～型。～义。～都（dū）。～稿。～数（shù）（ａ．规定数额；ｂ．指天命；ｃ．规定的数额）。断～。规～。鉴～。 ◎ 使不变动：～案。～罪。决～。确～。 ◎ 平安，平靖（多指局势）：大局已～。 ◎ 镇静，安稳（多指情绪）：心神不～。 ◎ 确凿，必然的：必～。镇～。 ◎ 预先约妥：～计。～情。～货。～做。 ◎ 姓。 订 （訂） dìng ◎ 改正，修改：～正。考～。校（jiào ）～。修～。 ◎ 约定，立（契约）：～立。～购。～约。 ◎ 用线、铁丝、书钉把书页、纸张连在一起：装～。 ◎ 制定：～计划。 these webside , http://www.zdic.net/zd/zi/ZdicE5ZdicAEZdic9A.htm http://www.zdic.net/zd/zi/ZdicE5ZdicAEZdic9A.htm hope it is hopeful

to sign with your name = 签名 I've never seen 定 or 订 used for "sign".