两个词的意义很近似,又都有“首先”、“第一”之意,但使用场合不尽一致.First的使用范围较大,可以作名词、形容词和副词,有时还可以代替firstly使用；firstly的运用范围较小,只能作副词,用于列举事实或理由的场合.汉语里的“首先”、“第一”,在英语中是firstly、first of all、in the first place或干脆说first；但汉语中的“最后一点”,英语里却不说last,而是说lastly或last of all,这是应当记住的.下面是first和firstly通用的例句：First（or Firstly）,we dice the pork and marinate it and,second （or secondly）,we prepare the dough for the pie． 首先,把猪肉切成肉丁并加醃料；其次是预备做馅饼的麦粉.但在下列场合里,first却不可以和firstly替换使用：We first（不能用firstly）go to Shenzhen,and then to Beijing． 我们先到深圳,然后上北京.He who would eat the nut must first（不能用firstly）crack the shell． 要吃核果,必须先破壳.下面是first作名词和形容词的例句：The first of May is International Labour Day． 五月一日是国际劳动节.The first question is whether the Government is willing to improve elementary education． 第一个问题是：政府是否愿意改造小学教育.通过上列的一些例句,我们可以看到,firstly只能用作副词,并只能用于列举事物和理由的场合.在现代英语中,firstly不如first用得普遍,许多人在列举事物时都是说：First,…；secondly,…；thirdly,….

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Firstly, secondly, thirdly, etc.
Because ordinal numbers (i.e., first, second, third, fourth, etc.) function as both adjectives and adverbs, the -ly adverbs firstly, secondly, thirdly, fourthly, and so on are superfluous. But despite the longstanding superstition against using them, these words are common in all types of writing, and there's no need to avoid them. Where they become troublesome, however, is when the numbers get above fourthly or fifthly (seventhly? eleventhly? sixteenthly?).
In the first place, in the second place, etc. are unnecessarily wordy. One, two, three, etc. are even more informal than first, second, third, etc.

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英语写文章时First,....Second,… .Third....和Firstly,....Secondly,… .Thirdly....一样的意思么?都一样么?
都可以 后者适用于非常正式的文体
表示第一,第二.意思一想.
但,First,....Second,… .Third...用得多些,而:
首先 first of all, 第二步：secondly , 然后：and then ,接下来next, 最后finally更好一点.